RD SHARMA Solutions for Class 9 Maths Chapter 19 - Surface Areas and Volume of a Circular Cylinder

Revise your lessons with RD Sharma Solutions for CBSE Class 9 Maths Chapter 19 Surface Areas and Volume of a Circular Cylinder. Learn to find the total radiating surface in a hot water heating system by applying your knowledge of the curved surface area of a cylinder. Get accurate answers on MCQs related to a cylinder with a detailed explanation by experienced subject experts.

Also, revise different types of problems on the volume of a cylinder with TopperLearning’s CBSE Class 9 Mathematics textbook solutions. For complete revision, go through our well-made concept videos, online practice tests, Maths question papers and more.

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Chapter 19 - Surface Areas and Volume of a Circular Cylinder Exercise Ex. 19.1

Question 1
Curved surface area of a right circular cylinder is 4.4 m2. If the radius of the base of the cylinder is 0.7 m, find its height.

Solution 1
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder
Question 2
In a hot water heating system, there is a cylindrical pipe of length 28 m and diameter 5 cm. Find the total radiating surface in the system.
Solution 2
 Height (h) of cylindrical pipe = Length of cylindrical pipe = 28 m
  Radius (r) of circular end of pipe = Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder cm = 2.5 cm = 0.025 m
  CSA of cylindrical pipe = Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder = 4.4 Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder
    Thus, the area of radiating surface of the system is 4.4 m2 or 44000 cm2.

Question 3
A cylindrical pillar is 50 cm in diameter and 3.5 m in height. Find the cost of painting the curved surface of the pillar at the rate of Rs.12.50 per m2.
Solution 3
Height of the pillar = 3.5 m
Radius of the circular end of the pillar =Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder cm = 25 cm  = 0.25 m
CSA of pillar = Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder = Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder
Cost of painting 1 Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder area = Rs 12.50
Cost of painting 5.5 Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder area = Rs (5.5 Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder12.50) = Rs 68.75

Thus, the cost of painting the CSA of pillar is Rs 68.75.

Question 4
It is required to make a closed cylindrical tank of height 1 m and base diameter 140 cm from a metal sheet. How many square meters of the sheet are required for the same?   
Solution 4
Height (h) of cylindrical tank = 1 m.
    Base radius (r) of cylindrical tank = Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder = 70 cm = 0.7 m

Area of sheet required = total surface area of tank = Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder   
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

So, it will require 7.48 Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinderof metal sheet.

Question 5

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Solution 5

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Question 6

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Solution 6

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Question 7

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Solution 7

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Question 8

The inner diameter of a circular well is 3.5 m. It is 10 m deep. Find

 (i)    Its inner curved surface area,
 (ii)    The cost of plastering this curved surface at the rate of Rs 40 per m2

Solution 8
Inner radius (r) of circular well = 1.75 m
Depth (h) of circular well = 10 m 
(i) Inner curved surface area = Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder
 

          Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder                            
          = (44 x 0.25 x 10) Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder
          = 110 m2
(ii) Cost of plastering 1 m2 area = Rs 40                    
    Cost of plastering 110 m2 area = Rs (110 x 40) = Rs 4400

Question 9
The students of a Vidyalaya were asked to participate in a competition for making and decorating penholders in the shape of a cylinder with a base, using cardboard. Each penholder was to be of radius 3 cm and height 10.5 cm. The Vidyalaya was to supply the competitors with cardboard. If there were 35 competitors, how much cardboard was required to be bought for the competition?   
Solution 9
Radius of circular end of cylindrical penholder = 3 cm
Height of penholder = 10.5 cm
Surface area of 1 penholder = CSA of penholder + Area of base of     
SA of 1 penholder = Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder + Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder                  
Area of cardboard sheet used by 1 competitor = Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder 
    Area of cardboard sheet used by 35 competitors

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder = 7920 cm2
    Thus, 7920 cm2 of cardboard sheet will be required for the competition.


Question 10

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Solution 10

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Question 11

Twenty cylindrical pillars of the Parliament House are to be cleaned. If the diameter of each pillar is 0.50 m and height is 4 m. What will be the cost of cleaning them at the rate of Rs 2.50 per square metre?

Solution 11

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Question 12

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Solution 12

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Question 13

The total surface area of a hollow metal cylinder open at both ends of external radius 8 cm and height 10 cm is 338Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder cm2. Taking r to be inner radius, obtain an equation in r and use it to obtain the thickness of the metal in the cylinder.

Solution 13

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Question 14

Find the lateral or curved surface area of a cylindrical petrol storage tank that is 4.2 m in diameter and 4.5 m high. How much steel was actually used, if Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder of the steel actually used was wasted in making the closed tank?

Solution 14
Height (h) cylindrical tank = 4.5 m
Radius (r) of circular end of cylindrical tank =Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinderm = 2.1m
    (i)    Lateral or curved surface area of tank = Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

                                    = Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder                                         
                                    = 59.4 m2            
    
    (ii)    Total surface area of tank = 2Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder (r + h)

              = Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder                           
              = 87.12 m2

    Let A m2 steel sheet be actually used in making the tank.

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder    
    
Thus, 95.04 Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder steel was used in actual while making the tank.    

Chapter 19 - Surface Areas and Volume of a Circular Cylinder Exercise Ex. 19.2

Question 1
A soft drink is available in two packs -

(i) a tin can with a rectangular base of length 5 cm and width 4 cm, having a height of 15 cm and
(ii) a plastic cylinder with circular base of diameter 7 cm and height 10 cm. Which container has greater capacity and by how much?   
Solution 1
The tin can will be cuboidal in shape.
Length (l) of tin can = 5 cm
Breadth (b) of tin can = 4 cm
Height (h) of tin can = 15 cm
Capacity of tin can = l Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular CylinderRd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder h = (5 Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular CylinderRd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder 15) cm3 = 300 cm3
Radius (R) of circular end of plastic cylinder = Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder
Height (H) of plastic cylinder = 10 cm
Capacity of plastic cylinder = Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular CylinderR2H  =Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder=385 cm3
Thus, the plastic cylinder has greater capacity.
Difference in capacity = (385 - 300) cm3 = 85 cm3

Question 2
The pillars of a temple are cylindrically shaped. If each pillar has a circular base of radius 20 cm and height 10m. How much concrete mixture would be required to build 14 such pillars?

Solution 2
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder
Question 3
The inner diameter of a cylindrical wooden pipe is 24 cm and its outer diameter is 28 cm. The length of the pipe is 35 cm. find the mass of the pipe, if 1 cm3 of wood has a mass of 0.6 g.
Solution 3
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder
Question 4
If the lateral surface of a cylinder is 94.2 cm2 and its height is 5 cm, then find
(i) radius of its base    (ii) its volume. (Use Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder = 3.14)
Solution 4
(i)    Height (h) of cylinder = 5 cm
        Let radius of cylinder be r.
        CSA of cylinder = 94.2 cm2
        2Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinderrh = 94.2 cm2
        (2 Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder 3.14 Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular CylinderRd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder 5) cm = 94.2 cm2
        r = 3 cm
 
(ii)    Volume of cylinder = Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinderr2h = (3.14 Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder (3)2 Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder 5) cm3 = 141.3 cm3

Question 5
The capacity of a closed cylindrical vessel of height 1 m is 15.4 litres. How many square metres of metal sheet would be needed to make it?
Solution 5
Let radius of the circular ends of the cylinder be r.
Height (h) of the cylindrical vessel = 1 m
Volume of cylindrical vessel = 15.4 litres = 0.0154 m3
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder
Total  Surface area of vessel = 2Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder r(r+h)
                                         Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder   
Thus, 0.4708 m2 of metal sheet would be needed to make the cylindrical vessel.   
Question 6
A patient in a hospital is given soup daily in a cylindrical bowl of diameter 7 cm. If the bowl is filled with soup to a height of 4 cm, how much soup the hospital has to prepare daily to serve 250 patients?
Solution 6
Radius (r) of cylindrical bowl = Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylindercm = 3.5 cm
Height (h) up to which the bowl is filled with soup = 4 cm
Volume of soup in 1 bowl = Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinderr2h= Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder 
Volume of soup in 250 bowls = (250 Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder 154) cm3 = 38500 cm3 = 38.5 litres

Thus, the hospital will have to prepare 38.5 litres of soup daily to serve 250 patients.

Question 7
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder
Solution 7
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder
Question 8

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Solution 8

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Question 9

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Solution 9

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Question 10

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Solution 10

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Question 11

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Solution 11

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Question 12

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Solution 12

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Question 13

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Solution 13

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Question 14

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Solution 14

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Question 15

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Solution 15

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Question 16

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Solution 16

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Question 17

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Solution 17

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Question 18

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Solution 18

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Question 19

A cylinderical container with diameter of base 56 cm contains sufficient water to submerge a rectangular solid of iron with dimensions 32 cm x 22 cm x 14 cm. Find the rise in the level of the water when the solid is completely submerged.

Solution 19

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Question 20

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Solution 20

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Question 21

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Solution 21

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Question 22

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Solution 22

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Question 23

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Solution 23

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Question 24

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Solution 24

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Question 25

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Solution 25

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Question 26

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Solution 26

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Question 27

A well with 14 m diameter is dug 8 m deep. The earth taken out of it has been evenly spread all around it to around it to a width of 21 m to form an embankment. Find the height of the embankment.

Solution 27

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Question 28

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Solution 28

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Question 29

Water flows out through a circular pipe whose internal diameter is 2 cm, at the rate of 6 meters per second into cylindrical tank. The water is collected in a cylindrical vessel radius of whose base is 60 cm. Find the rise in the level of water in 30 minutes?

Solution 29

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Question 30

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Solution 30

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Question 31

The sum of the radius of the base and height of a solid cylinder is 37 m. If the total surface area of the solid cylinder is 1628 m2. Find the volume of the cylinder.

Solution 31

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Question 32
A well with 10 m inside diameter is dug 8.4 m deep. Earth taken out of it is spread all around it to a width of 7.5 m to form an embankment. Find the height of the embankment.
Solution 32
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Chapter 19 - Surface Areas and Volume of a Circular Cylinder Exercise 19.28

Question 1

In a cylinder, if radius is doubled and height is halved, curved surface area will be

(a) halved

(b) doubled

(c) same

(d) four times

Solution 1

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Question 2

Two cylindrical jars have their diameters in the ratio 3 : 1, but height 1 : 3. Then the ratio of their volumes is

(a) 1 : 4

(b) 1 : 3

(c) 3 : 1

(d) 2 : 5

Solution 2

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Question 3

The number of surfaces in right cylinder is

(a) 1

(b) 2

(c) 3

(d) 4

Solution 3

Number of Surfaces In a Right cylinder are 3.

Top surface, bottom surface and curved surface.

Hence, correct option is (c).

Question 4

Vertical cross-section of a right circular cylinder is always a

(a) square

(b) rectangle

(c) rhombus

(d) trapezium

Solution 4

Vertical cross-section of cylinder will always be a Rectangle of sides 'h', and 'r',

where h is the height of a cylinder and r is the radius of a cylinder.

Hence, correct option is (b).

Question 5

If r is the radius and h is height of the cylinder the volume will be

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Solution 5

Volume of cylinder

= Area of Base × Height

= (∏r2) × h

V = ∏r2h

Hence, correct option is (b).

Question 6

The number of surfaces of a hollow cylindrical object is

(a) 1

(b) 2

(c) 3

(d) 4

Solution 6

A Hollow cylinder has only 2 surfaces.

One is outer-curved surface and another is inner-curved surface.

Hence, correct option is (b).

Chapter 19 - Surface Areas and Volume of a Circular Cylinder Exercise 19.29

Question 7

If the radius of a cylinder is doubled and the height remains same, the volume will be

(a) doubled

(b) halved

(c) same

(d) four times

Solution 7

Volume  of a cylinder = V = ∏r2h

If r' = 2r and h' = h, then

V' = ∏(2r)2h   = 4∏r2h

V' = 4V

Hence, correct option is (d).

Question 8

If the height of a cylinder is doubled and radius remains the same, then volume will be

(a) doubled

(b) halved

(c) same

(d) four times 

Solution 8

Volume of cylinder V = ∏r2h

If h' = 2h and r' = r, then

V' = ∏(r)2(2h) = 2∏r2h = 2V

Hence, correct option is (a).

Question 9

In a cylinder, if radius is halved and height is doubled, the volume will be

(a) same

(b) doubled

(c) halved

(d) four times

Solution 9

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Question 14

If the height of a cylinder is doubled, by what number must the radius of the base be multiplied so that the resulting cylinder has the same volume as the original cylinder?

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Solution 14

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Question 15

The volume of a cylinder of radius r is 1/4 of the volume of a rectangular box with a square base of side length x. If the cylinder and the box have equal heights, what is r in terms of x?

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Solution 15

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Question 16

The height h of a cylinder equals the circumference of the cylinder. In terms of h, what is the volume of the cylinder?

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Solution 16

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Question 10

If the diameter of the base of a closed right circular cylinder be equal to its height h, then its whole surface area is

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Solution 10

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Question 11

A right circular cylindrical tunnel of diameter 2 m and length 40 m is to be constructed from a sheet of iron. The area of the iron sheet required in m2, is

(a) 40∏

(b) 80∏

(c) 160∏

(d) 200∏

Solution 11

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Question 12

Two circular cylinders of equal volume have their heights in the ratio 1 : 2. Ratio of their radii is

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Solution 12

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Question 13

The radius of a wire is decreased to one-third. If volume remains the same, the length will become

(a) 3 times

(b) 6 times

(c) 9 times

(d) 27 times

Solution 13

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Question 17

A cylinder with radius r and height h is closed on the top and bottom. Which of the following expressions represents the total surface area of this cylinder?

(a) 2∏r (r + h)

(b) ∏r (r + 2h)

(c) ∏r (2r + h)

(d) 2∏r+ h

Solution 17

Total surface Area = Area of Top + Area of bottom + Curved Surface Area

T.S.A. = ∏r2 + ∏r2 + 2∏rh = 2∏r2 + 2∏rh = 2∏r (r + h)

Hence, correct option is (a).

Chapter 19 - Surface Areas and Volume of a Circular Cylinder Exercise 19.30

Question 18

The height of sand in a cylindrical-shaped can drops 3 inches when 1 cubic foot of sand is poured out. What is the diameter, in inches, of the cylinder?

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Solution 18

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Question 19

Two steel sheets each of length a1 and breadth a2 are used to prepare the surfaces of two right circular cylinders - one having volume v1 and height a2 and other having volume v2 and height a1. Then,

(a) v1 = v2

(b) a1v1 = a2v2

(c) a2v1 = a1v2

(d) Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder 

Solution 19

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Question 20

The altitude of a circular cylinder is increased six times and the base area is decreased one-ninth of its value. The factor by which the lateral surface of the cylinder increases, is

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder

Solution 20

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Circular Cylinder