RD SHARMA Solutions for Class 9 Maths Chapter 18 - Surface Areas and Volume of a Cuboid and Cube

Get enough chapter practice with TopperLearning’s RD Sharma Solutions for CBSE Class 9 Maths Chapter 18 Surface Areas and Volume of a Cuboid and Cube. Get model answers for textbook questions on finding the lateral surface area of a cuboid. Figure out how to perform a calculation of the total surface area of small cubes which are created by cutting a large cube.

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Chapter 18 - Surface Areas and Volume of a Cuboid and Cube Exercise Ex. 18.1

Question 1
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube
Solution 1
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube
Question 2

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Solution 2

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Question 3
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube
Solution 3
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube
Question 4
Mary wants to decorate her Christmas tree. She wants to place the tree on a wooden block covered with coloured paper with picture of Santa Claus on it. She must know the exact quantity of paper to buy for this purpose. If the box has length, breadth and height as 80 cm, 40 cm and 20 cm respectively. How many square sheets of paper of side 40 cm would she require?

Solution 4
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube
Question 5

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Solution 5
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube
Question 6
Three equal cubes are placed adjacently in a row. Find the ratio of total surface area of the new cuboid to that of the sum of the surface areas of the three cubes.
Solution 6
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube
Question 7
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube
Solution 7
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube
Question 8
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube
Solution 8
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube
Question 9
Hameed has built a cubical water tank with lid for his house, with each outer edge 1.5 m long. He gets the outer surface of the tank excluding the base, covered with square tiles of side 25 cm. Find how much he would spend for the titles, if the cost of tiles is Rs. 360 per dozen.
Solution 9
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube
Question 10
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube
Solution 10
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube
Question 11

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Solution 11

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Question 12

Ravish wanted to make a temporary shelter for his car, by making a box-like structure with tarpaulin that covers all the four sides and the top of the car (with the front face as a flap which can be rolled up). Assuming that the stitching margins are very small, and therefore negligible, how much tarpaulin would be required to make the shelter of height 2.5 m, with base dimensions 4 m x 3m?

Solution 12
Length of shelter = 4 m
Breadth of shelter = 3 m
Height of shelter = 2.5 m

The tarpaulin will be required for top and four sides of the shelter.
Area of Tarpaulin required = 2(lh + bh) + lb
= [2(4 Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube 2.5 + 3 Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube 2.5) + 4 Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube 3] m2
= [2(10 + 7.5) + 12] m2
= 47 m2


Question 13

An open box is made of wood 3 cm thick. Its external length, breadth and height are 1.48m, 1.16 m and 8.3 dm. Find the cost of painting the inner surface at Rs 50 per sq meter.

Solution 13

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Question 14

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Solution 14

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Question 15
The paint in a certain container is sufficient to paint an area equal to 9.375 m2. How many bricks of dimensions 22.5 cm × 10 cm × 7.5 cm can be painted out of this container?
Solution 15
Total surface area of one brick = 2(lb + bh + lh)
 = [2(22.5 × 10 + 10 × 7.5 + 22.5 × 7.5)]cm2
 = 2(225 + 75 + 168.75) Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube
          = (2 × 468.75) cm2
 = 937.5 cm2   
Let n number of bricks be painted by the container.
Area of n bricks = 937.5n cm2   
Area that can be painted by the container = 9.375 m2 = 93750 cm2
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube 93750 = 937.5n
n = 100
Thus, 100 bricks can be painted out by the container.

 

Question 16

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Solution 16

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Question 17

The cost of preparing the walls of a room 12 m long at the rate of Rs 1.35 per square meter is Rs 340.20 and the cost of matting the floor at 85 paise per square meter is Rs 91.80. Find the height of the room.

Solution 17

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Question 18

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Solution 18

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Question 19
A wooden bookshelf has external dimensions as follows: Height = 110 cm, Depth = 25 cm, Breadth = 85 cm. The thickness of the plank is 5 cm everywhere. The external faces are to be polished and the inner faces are to be painted. If the rate of polishing is 20 paise per cm2 and the rate of painting is 10 paise per cm2, find the total expenses required for polishing and painting the surface of the bookshelf.
 
                                           Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube
Solution 19
    External length (l) of bookshelf = 85 cm
    External breadth (b) of bookshelf = 25 cm
    External height (h) of bookshelf = 110 cm
    External surface area of shelf while leaving front face of shelf
                                                  = lh + 2 (lb + bh)
                                                  = [85 Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube 110 + 2 (85 Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube 25 + 25 Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube 110)] cm2
                                                  = 19100 cm2
    Area of front face = [85 Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube 110 - 75 Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube 100 + 2 (75 Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube 5)] cm2
                                                  = 1850 + 750 cm2
                                                  = 2600 cm2
    Area to be polished = (19100 + 2600) cm2 = 21700 cm2    
    Cost of polishing 1 cm2 area = Rs 0.20
    Cost of polishing 21700 cm2 area = Rs (21700 Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube 0.20) = Rs 4340    
    
    Now, length (l), breadth (b) height (h) of each row of bookshelf is 75 cm, 20 cm, and
    30cm Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube respectively.
    Area to be painted in 1 row = 2 (l + h) b + lh
                                           = [2 (75 + 30) Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube 20 + 75 Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube 30] cm2
                                           = (4200 + 2250) cm2
                                           = 6450 cm2    
    Area to be painted in 3 rows = (3 Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube 6450) cm2 = 19350 cm2
    Cost of painting 1 cm2 area = Rs 0.10
    Cost of painting 19350 cm2 area = Rs (19350 Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube 0.10) = Rs 1935    
    Total expense required for polishing and painting the surface of the bookshelf 
                                            = Rs(4340 + 1935) = Rs 6275

Chapter 18 - Surface Areas and Volume of a Cuboid and Cube Exercise Ex. 18.2

Question 1
A cuboidal water tank is 6 m long, 5 m wide and 4.5 m deep. How, many litres of water can it holds? 
Solution 1
Volume of tank = l Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube b Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube h = (6 Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube 5 Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube 4.5) m3 = 135 m3
  It is given that:
 1 m3 = 1000 litres
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube
    
 Thus, the tank can hold 135000 litres of water.

Question 2
A cuboidal vessel is 10 m long and 8 m wide. How high must it be made to hold 380 cubic metres of a liquid?   
Solution 2
Let height of cuboidal vessel be h.
Length (l) of vessel = 10 m
Width (b) of vessel = 8 m
Volume of vessel = 380 m3
 Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And CubeRd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube b Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube h = 380 
       
 10 Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube 8 Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube h = 380
 h = 4.75
    
 Thus, the height of the vessel should be 4.75 m.    

Question 3
Find the cost of digging a cuboidal pit 8 m long, 6 m broad and 3 m deep at the rate of Rs 30 per m3.

Solution 3
Length (l) of the cuboidal pit = 8 m
Width (b) of the cuboidal pit = 6 m
 Depth (h) of the cuboidal pit = 3 m
Volume of the cuboidal pit = l Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube b Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube h = (8 Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube 6 Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube 3) Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube = 144 m3  
Cost of digging 1 m3 = Rs 30
Cost of digging 144 m3 = Rs (144 Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube30) = Rs 4320

Question 4

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Solution 4

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Question 5

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Solution 5

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Question 6

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Solution 6

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Question 7

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Solution 7

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Question 8

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Solution 8

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Question 9

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Solution 9

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Question 10

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Solution 10

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Question 11

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Solution 11

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Question 12

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Solution 12

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Question 13

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Solution 13

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Question 14

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Solution 14

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Question 15

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Solution 15

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Question 16
A village, having a population of 4000, requires 150 litres of water per head per day. It has a tank measuring 20 m × 15 m × 6 m. For how many days will the water of this tank last?
Solution 16
Length (l) of the cuboidal tank = 20 m
Breadth (b) of the cuboidal tank = 15 m
Height (h) of the cuboidal tank = 6 m

Capacity of tank = l × b × h    = (20 × 15 × 6) m3 = 1800 m3 = 1800000 litres

Water consumed by people of village in 1 day = 4000 × 150 litres = 600000 litres

Let water of this tank lasts for n days.
Water consumed by all people of village in n days = capacity of tank
n × 600000 = 1800000
n = 3    
Thus, the water of tank will last for 3 days.

Question 17

A child playing with building blocks, which are of the shape of the cubes, has built a structure as shown in fig. If the edge of each cube is 3 cm, find the volume of the structure built by the child

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Solution 17

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Question 18
A godown measures 40 m Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube 25 m Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube 10 m. Find the maximum number of wooden crates each measuring 1.5 m Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube 1.25 m Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube 0.5 m that can be stored in the godown.    

Solution 18
Length Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube of the godown = 40 m
    Breadth Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube of the godown = 25 m
    Height Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube of the godown = 10 m

Volume of godown = l1 Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube b1Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube h1 = (40 Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube 25 Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube 10) Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube = 10000 Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube    

    Length Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube of a wooden crate = 1.5 m
    Breadth Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube of a wooden crate = 1.25 m
    Height Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube of a wooden crate = 0.5 m

Volume of a wooden crate = Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube = (1.5 Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube 1.25 Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube 0.5) m3 = 0.9375 Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Let n wooden crates be stored in the godown.
Volume of n wooden crates = volume of godown
0.9375 Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube n = 10000

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube 

Thus, 10666 wooden crates can be stored in godown.

Question 19

A wall of length 10 m was to be built across an open ground. The height of the wall is 4 m and thickness of the wall is 24 cm. If this wall is to be built up with bricks whose dimensions are 24 cm x 12 cm x 8 cm, how many bricks would be required?

Solution 19

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Question 20

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Solution 20

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Question 21

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Solution 21

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Question 22
A river 3 m deep and 40 m wide is flowing at the rate of 2 km per hour. How much water will fall into the sea in a minute?
Solution 22
Rate of water flow = 2 km per hour  Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube
Depth (h) of river = 3 m
Width (b) of river = 40 m
Volume of water flowed in 1 min Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube 
Thus, in 1 minute 4000 Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube = 4000000 litres of water will fall into the sea.    

Question 23

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Solution 23

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Question 24

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Solution 24

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Question 25

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Solution 25

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Question 26

A rectangular container, whose base is a square of side 5 cm, stands on a horizontal table, and holds water upto 1 cm from the top. When a cube is placed in the water it is completely submerged, the water rises to the top and 2 cubic cm of water overflows. Calculate the volume of the cube and also the length of its edge.

Solution 26

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Question 27

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Solution 27

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Question 28

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Solution 28

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Chapter 18 - Surface Areas and Volume of a Cuboid and Cube Exercise 18.35

Question 1

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Solution 1

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Question 2

Three equal cubes are placed adjacently in a row. The ratio of the total surface area of the resulting cuboid to that of the sum of the surface areas of three cubes, is

(a) 7 : 9

(b) 49 : 81

(c) 9 : 7

(d) 27 : 23

Solution 2

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Question 3

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Solution 3

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Question 4

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Solution 4

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Question 5

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Solution 5

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Question 6

The length, width and height of a rectangular solid are in the ratio of 3 : 2 : 1. If the volume of the box is 48 cm3, the total surface area of the box is

(a) 27 cm2

(b) 32 cm2

(c) 44 cm2

(d) 88 cm2

Solution 6

Let,

Length = 3x,

Width = 2x

Height = x

Volume = 48 cm3

L×W×H = 48 cm3

3x × 2x × x = 48 cm3

6x3 = 48 cm3

x3 = 8 cm3

x = 2 cm

Total Surface area

= 2(3x × 2x + 2x × x + 3x × x)

= 2(6x2 + 2x2 + 3x2

= 2(11x2)

= 22x2

= 22(4)

= 88 cm2

Hence, correct option is (d).

Question 7

If the areas of the adjacent faces of a rectangular block are in the ratio 2 : 3 : 4 and the volume is 9000 cm3, then the length of the shortest edge is

(a) 30 cm

(b) 20 cm

(c) 15 cm

(d) 10 cm

Solution 7

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Chapter 18 - Surface Areas and Volume of a Cuboid and Cube Exercise 18.36

Question 8

If each edge of a cube, of volume V, is doubled, then the volume of the new cube is

(a) 2 V

(b) 4 V

(c) 6 V

(d) 8 V

Solution 8

Let edge = a

Volume, V = a3

If a' = 2a, then

V' = (a')3 = (2a)3 = 8a3

V' = 8 V

Hence, correct option is (d).

Question 9

If each edge of a cuboid of surface area S is doubled, then surface area of the new cuboid is

(a) 2 S

(b) 4 S

(c) 6 S

(d) 8 S

Solution 9

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Question 10

The area of the floor of a room is 15 m2. If its height is 4 m, then the volume of the air contained in the room is

(a) 60 dm3

(b) 600 dm3

(c) 6000 dm3

(d) 60000 dm3

Solution 10

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Question 11

The cost of constructing a wall 8 m long, 4 m high and 20 cm thick at the rate of Rs. 25 per m3 is

(a) Rs. 16

(b) Rs. 80

(c) Rs. 160

(d) Rs. 320

Solution 11

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Question 12

10 cubic metres clay is uniformly spread on a land of area 10 ares. The rise in the level of the ground is

(a) 1 cm

(b) 10 cm

(c) 100 cm

(d) 1000 cm

Solution 12

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Question 13

Volume of a cuboid is 12 cm3. The volume (in cm3) of a cuboid whose sides are double of the above cuboid is

(a) 24

(b) 48

(c) 72

(d) 96

Solution 13

Let the dimensions of Cuboid be a, b, c respectively.

Volume, V = abc = 12 cm3

If a' = 2a,   b' = 2b,   c' = 2c, then 

V' = a'b'c' = 8abc = 8 × 12 = 96 cm3

Hence, correct option is (d).

Question 14

If the sum of all the edges of a cube is 36 cm, then the volume (in cm3) of that cube is

(a) 9

(b) 27

(c) 219

(d) 729

Solution 14

Let the edge of cube = a

Total no. of edge = 12

Sum of all edges = 12a

12a = 36cm

i.e. a = 3 cm

Volume = a3 = 33 = 27 cm3

Hence, correct option is (b).

Question 15

The number of cubes of sides 3 cm that can be cut from a cuboid of dimensions 10 cm × 9 cm × 6 cm, is

(a) 9

(b) 10

(c) 18

(d) 20

Solution 15

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Question 16

On a particular day, the rain fall recorded in a terrace 6 m long and 5 m broad is 15 cm. The quantity of water collected in the terrace is

(a) 300 litres

(b) 450 litres

(c) 3000 litres

(d) 4500 litres

Solution 16

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Question 17

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Solution 17

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Question 18

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Solution 18

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Question 19

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Solution 19

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Question 20

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Solution 20

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Question 21

If each edge of a cube is increased by 50%, the percentage increase in its surface area is

(a) 50%

(b) 75%

(c) 100%

(d) 125%

Solution 21

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube

Chapter 18 - Surface Areas and Volume of a Cuboid and Cube Exercise 18.37

Question 22

A cube whose volume is 1/8 cubic centimeter is placed on top of a cube whose volume is 1 cm3. The two cubes are then placed on top of a third cube whose volume is 8 cm3. The height of the stacked cubes is

(a) 3.5 cm

(b) 3 cm

(c) 7 cm

(d) none of these

Solution 22

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Cuboid And Cube