SELINA Solutions for Class 9 Maths Chapter 21 - Solids [Surface Area and Volume of 3-D Solids]

Learn to find the volume and the surface area of a given cube with our Selina Solutions for ICSE Class 9 Maths Chapter 21 Solids - Surface Area and Volume of 3-D Solids. TopperLearning’s model answers by experts can help you to revise the textbook exercises with ease. Understanding the structure of solids such as cube, cuboid etc. is easy when you have accurate answers.

Our ICSE Class 9 Mathematics Selina solutions can assist you with revision of topics like volume of a cuboid, area of a cross-section etc. For more clarity, go through the online doubts and solutions available for Class 9 round the clock at our learning portal.

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Chapter 21 - Solids [Surface Area and Volume of 3-D Solids] Exercise Ex. 21(C)

Question 1

Each face of a cube has perimeter equal to 32 cm. Find its surface area and its volume.

Solution 1

The perimeter of a cube formula is, Perimeter = 4a where (a= length)

Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

 

 

 

 

Question 2

A school auditorium is 40 m long, 30 m broad and 12 m high. If each student requires 1.2 m2 of the floor area; find the maximum number of students that can be accommodated in this auditorium. Also, find the volume of air available in the auditorium, for each student.

Solution 2

Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

Question 3

The internal dimensions of a rectangular box are 12 cm Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solidsx cm Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids9 cm. If the length of the longest rod that can be placed in this box is 17 cm; find x.

Solution 3

Length of longest rod=Length of the diagonal of the box

Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

Question 4

The internal length, breadth and height of a box are 30 cm, 24 cm, and 15 cm. Find the largest number of cubes which can be placed inside this box if the edge of each cube is

(i) 3 cm(ii) 4 cm(iii) 5 cm

Solution 4

(i)

No. of cube which can be placed along lengthSelina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids.

No. of cube along the breadthSelina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

No. of cubes along the heightSelina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids.

Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D SolidsThe total no. of cubes placedSelina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

(ii)

Cubes along lengthSelina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

Cubes along widthSelina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solidsand cubes along heightSelina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D SolidsThe total no. of cubes placedSelina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

(iii)

Cubes along lengthSelina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

Cubes along widthSelina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solidsand cubes along heightSelina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D SolidsThe total no. of cubes placedSelina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

Question 5

A rectangular field is 112 m long and 62 m broad. A cubical tank of edge 6 m is dug at each of the four corners of the field and the earth so removed is evenly spread on the remaining field. Find the rise in level.

Solution 5

Vol. of the tank= vol. of earth spread

Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

Question 6

When length of each side of a cube is increased by 3 cm, its volume is increased by 2457 cm3. Find its side. How much will its volume decrease, if length of each side of it is reduced by 20%?

Solution 6

Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

 

 

 

 

Question 7

A rectangular tank 30 cm × 20 cm × 12 cm contains water to a depth of 6 cm. A metal cube of side 10 cm is placed in the tank with its one face resting on the bottom of the tank. Find the volume of water, in litres, that must be poured in the tank so that the metal cube is just submerged in the water.

Solution 7

Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids 

Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

 

Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids 

Question 8

The dimensions of a solid metallic cuboid are 72 cm × 30 cm × 75 cm. It is melted and recast into identical solid metal cubes with each of edge 6 cm. Find the number of cubes formed.

Also, find the cost of polishing the surfaces of all the cubes formed at the rate Rs. 150 per sq. m.

Solution 8

Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

 

 

 

 

Question 9

The dimensions of a car petrol tank are 50 cm × 32 cm × 24 cm, which is full of petrol. If car's average consumption is 15 km per litre, find the maximum distance that can be covered by the car.

Solution 9

Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

 

 

 

 

Question 10

The dimensions of a rectangular box are in the ratio 4 : 2 : 3. The difference between cost of covering it with paper at Rs. 12 per m2 and with paper at the rate of 13.50 per m2 is Rs. 1,248. Find the dimensions of the box.

Solution 10

Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

 

Chapter 21 - Solids [Surface Area and Volume of 3-D Solids] Exercise Ex. 21(A)

Question 1

Four identical cubes are joined end to end to form a cuboid. If the total surface area of the resulting cuoid as 648 m2; find the length of edge of each cube.

Also, find the ratio between the surface area of resulting cuboid and the surface area of a cube.

Solution 1

Let l be the length of the edge of each cube.

The length of the resulting cuboid=Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

Let width (b) = l cm and its height (h)= l cm

Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D SolidsThe total surface area of the resulting cuboid

Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

Therefore, the length of each cube is 6 cm.

Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

Question 2

The volume of a cube is 729 cm3. Find its total surface area.

Solution 2

Let a be the one edge of a cube.

VolumeSelina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

Total surface area=6Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

Question 3

The dimensions of a Cinema Hall are 100 m, 60 m and 15 m. How many persons can sit in the hall, if each requires 150 m3 of air?

Solution 3

Volume of cinema hallSelina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

150 Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solidsrequires= 1 person

90000Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solidsrequires=Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solidspersons

Therefore, 600 persons can sit in the hall.

Question 4

75 persons can sleep in a room 25 m by 9.6 m. If each persons requires 16 m3 of air; find the height of the room.

Solution 4

Let h be height of the room.

1 person requires 16Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

75 person requires Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

 

Volume of room is 1200Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

Question 5

The edges of three cubes of metal are 3 cm, 4 cm and 5 cm. They are melted and formed into a single cube. Find the edge of the new cube.

Solution 5

Volume of melted single cube Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

Let a be the edge of the new cube.

VolumeSelina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

Therefore, 6 cm is the edge of cube.

Question 6

Three cubes, whose edges are x cm, 8 cm and 10 cm respectively, are melted and recasted into a single cube of edge 12 cm. Find 'x'.

Solution 6

Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

Question 7

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

Solution 7

Let the side of a cube be 'a' units.

Total surface area of one cubeSelina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

Total surface area of 3 cubes Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

After joining 3 cubes in a row, length of Cuboid =3a

Breadth and height of cuboid = a

Total surface area of cuboid Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids 

Ratio of total surface area of cuboid to the total surface area of 3 cubesSelina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids 

Question 8

The cost of papering the four walls of a room at 75 paisa per square meter Rs. 240. The height of the room is 5 metres. Find the length and the breadth of the room, if they are in the ratio 5 : 3.

Solution 8

Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

Question 9

The area of a playground is 3650 m2. Find the cost of covering it with gravel 1.2 cm deep, if the gravel costs Rs. 6.40 per cubic metre.

Solution 9

The area of the playground is 3650 m2 and the gravels are 1.2 cm deep. Therefore the total volume to be covered will be:

3650 x 0.012 =43.8 m3.

Since the cost of per cubic meter is Rs. 6.40, therefore the total cost will be:

43.8 x Rs.6.40 = Rs.280.32

Question 10

A square plate of side 'x' cm is 8 mm thick. If its volume is 2880 cm3; find the value of x.

Solution 10

Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

Question 11

The external dimensions of a closed wooden box are 27 cm, 19 cm and 11 cm. If the thickness of the wood in the box is 1.5 cm; find:

(i) Volume of the wood in the box;

(ii) The cost of the box, if wood costs Rs. 1.20 per cm3;

(iii) Number of 4 cm cubes that could be placed into the box.

Solution 11

External volume of the box=Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

Since, external dimensions are 27 cm, 19 cm, 11 cm; thickness of the wood is 1.5 cm.

Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D SolidsInternal dimensions

Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

Hence, internal volume of box=Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

(i)

Volume of wood in the box=Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

(ii)

Cost of woodSelina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D SolidsSelina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

(iii)

Vol. of 4 cm cube=Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

Number of 4 cm cubes that could be placed into the box

Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

Question 12

A tank 20 m long, 12 m wide and 8 m deep is to be made of iron sheet. If it is open at the top. Determine the cost of iron-sheet, at the rate of Rs. 12.50 per metre, if the sheet is 2.5 m wide.

Solution 12

Area of sheet= Surface area of the tank

Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D SolidsLength of the sheetSelina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solidsits width=Area of 4 walls of the tank +Area of its base

Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D SolidsLength of the sheet Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids2.5 m=Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D SolidsLength of the sheet= 300.8 m

Cost of the sheet = 300.8 Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D SolidsRs 12.50 = Rs 3760

Question 13

A closed rectangular box is made of wood of 1.5 cm thickness. The exterior length and breadth are respectively 78 cm and 19 cm, and the capacity of the box is 15 cubic decimeters. Calculate the exterior height of the box.

Solution 13

Let exterior height is h cm. Then interior dimensions are 78-3=75, 19-3=16 and h-3 (subtract two thicknesses of wood). Interior volume = 75 x 16 x (h-3) which must = 15 cu dm

= 15000 cm^3

(1 dm = 10cm, 1 cu dm = 10^3 cm^3).

15000Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids= 75 x 16 x (h-3)

Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solidsh-3 = 15000/(75x16) = 12.5 cm Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solidsh = 15.5 cm.

Question 14

The square on the diagonal of a cube has an area of 1875 sq. cm. Calculate:

(i) The side of the cube.

(ii) The total surface area of the cube.

Solution 14

(i)

If the side of the cube= a cm

The length of its diagonal= Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solidscm

And,

Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

(ii)

Total surface area of the cube=Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

=Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

Question 15

A hollow square-shaped tube open at both ends is made of iron. The internal square is of 5 cm side and the length of the tube is 8 cm. There are 192 cm3 of iron in this tube. Find its thickness.

Solution 15

Given that the volume of the iron in the tube 192 cm3

Let the thickness of the tubeSelina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D SolidsSide of the external square=Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D SolidsExt. vol. of the tube Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solidsits internal vol.= volume of iron in the tube, we have,

Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

Therefore, thickness is 1 cm.

Question 16

Four identical cubes are joined end to end to form a cuboid. If the total surface area of the resulting cuoid as 648 m2; find the length of edge of each cube.

Also, find the ratio between the surface area of resulting cuboid and the surface area of a cube.

Solution 16

Let l be the length of the edge of each cube.

The length of the resulting cuboid=Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

Let width (b) = l cm and its height (h)= l cm

Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D SolidsThe total surface area of the resulting cuboid

Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

Therefore, the length of each cube is 6 cm.

Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

Chapter 21 - Solids [Surface Area and Volume of 3-D Solids] Exercise Ex. 21(B)

Question 1

The following figure shows a solid of uniform cross-section. Find the volume of the solid. All measurements are in centimetres.

Assume that all angles in the figures are right angles.

Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

Solution 1

The given figure can be divided into two cuboids of dimensions 6 cm, 4 cm, 3 cm, and 9 cm respectively. Hence, volume of solid

Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

Question 2

A swimming pool is 40 m long and 15 m wide. Its shallow and deep ends are 1.5 m and 3 m deep respectively. If the bottom of the pool slopes uniformly, find the amount of water in litres required to fill the pool.

Solution 2

Area of cross section of the solid

Volume of solid

Question 3

The cross-section of a tunnel perpendicular to its length is a trapezium ABCD as shown in the following figure; also given that:

AM = BN; AB = 7 m; CD = 5 m. The height of the tunnel is 2.4 m. The tunnel is 40 m long. Calculate:

Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

(i) The cost of painting the internal surface of the tunnel (excluding the floor) at the rate of Rs. 5 per m2 (sq. metre).

(ii) The cost of paving the floor at the rate of Rs. 18 per m2.

Solution 3

The cross section of a tunnel is of the trapezium shaped ABCD in which Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solidsand AM = BN. The height is 2.4 m and its length is 40m.

(i)

Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

Perimeter of the cross- section of the tunnel=Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

Length=40 m

Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D SolidsInternal surface area of the tunnel(except floor)

Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

Rate of painting=Rs 5 perSelina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

Hence, total cost of painting=Rs 5Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids408=Rs 2040

(ii)

Area of floor of tunnelSelina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

Rate of cost of pavingSelina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

Total cost=Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

Question 4

Water is discharged from a pipe of cross-section area 3.2 cm2 at the speed of 5m/s. Calculate the volume of water discharged:

(i) In cm3 per sec.

(ii) In litres per minute.

Solution 4

(i)

The rate of speed Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

Volume of water flowing per secSelina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

(ii)

Vol. of water flowing per minSelina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

Since 1000Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids= 1 lt

Therefore, Vol. of water flowing per min=Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

Question 5

A hose-pipe of cross-section area 2 cm2 delivers 1500 litres of water in 5 minutes. What is the speed of water in m/s through the pipe?

Solution 5

Vol. of water flowing in 1 sec=Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

Vol. of water flowing =area of cross sectionSelina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solidsspeed of water

Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

Question 6

The cross-section of a piece of metal 4 m in length is shown below. Calculate:

Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

(i) The area of the cross-section;

(ii) The volume of the piece of metal in cubic centimetres.

If 1 cubic centimetre of the metal weighs 6.6 g, calculate the weight of the piece of metal to the nearest kg.

Solution 6

Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

(i)

Area of total cross section= Area of rectangle abce+ area of Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

=Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

(ii)

The volume of the piece of metal in cubic centimeters= Area of total cross sectionSelina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

=Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

1 cubic centimetre of the metal weighs 6.6 g

Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solidsof the metal weighsSelina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

The weight of the piece of metal to the nearest Kg is 352 Kg.

Question 7

A rectangular water-tank measuring 80 cm Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids60 cm Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids60 cm is filled form a pipe of cross-sectional area 1.5 cm2, the water emerging at 3.2 m/s. How long does it take to fill the tank?

Solution 7

Vol. of rectangular tankSelina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

One liter= 1000Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

Vol. of water flowing in per sec=

Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

 

Vol. of water flowing in 1 min=Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

Hence,

Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solidscan be filled = 1 min

Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solidscan be filledSelina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

Question 8

A rectangular card-board sheet has length 32 cm and breadth 26 cm.Squares each of side 3 cm, are cut from the corners of the sheet and the sides are folded to make a rectangular container. Find the capacity of the container formed.

Solution 8

Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids 

Length of sheet=32 cm

Breadth of sheet=26 cm

Side of each square=3cm

Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D SolidsInner length=32-2Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids3=32-6=26 cm

Inner breadth=Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solidscm

By folding the sheet, the length of the container=26 cm

Breadth of the container= 20 cm and height of the container= 3 cm

Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D SolidsVol. of the container=Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

=Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

Question 9

A swimming pool is 18 m long and 8 m wide. Its deep and shallow ends are 2 m and 1.2 m respectively. Find the capacity of the pool, assuming that the bottom of the pool slopes uniformly.

Solution 9

Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

Length of pool= 18 m

Breadth of pool= 8 m

Height of one side= 2m

Height on second side=1.2 m

Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D SolidsVolume of pool=Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

Question 10

The following figure shows a closed victory-stand whose dimensions are given in cm.

 

 

 Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids 

 

 

Find the volume and the surface are of the victory stand.

 

 

 

Solution 10

Consider the box 1

 

 

Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

 

 

Thus, the dimensions of box 1 are: 60 cm, 40 cm and 30 cm.

 

 

Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

 

 

 

 

 

Consider the box 2

 

 

Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

 

 

Thus, the dimensions of box 2 are: 40 cm, 30 cm and 30 cm.

 

 

Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

 

 

 

 

 

Consider the box 3

 

 

 

 

 

Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

 

 

Thus, the dimensions of box 2 are: 40 cm, 30 cm and 20 cm.

 

 

Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids

 

 

 

 

 

Selina Solutions Icse Class 9 Mathematics Chapter - Solids Surface Area And Volume Of 3 D Solids