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Class 9 RD Sharma Solutions – Chapter 19 Surface Area And Volume of a Right Circular Cylinder – Exercise 19.2 | Set 1
  • Last Updated : 07 Apr, 2021

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 : 

Given that,

The tin can with a rectangular base:

Length= 5 cm,

Breadth = 4 cm,



Height = 15 cm

The plastic cylinder with circular base:

Diameter = 7cm

So the radius of the base = 7/2 cm = 3.5 cm

Height = 10 cm

Now we find the volume of both cans:

Capacity of the tin can = l × b × h = (5 × 4 x 15) cm3

Capacity of plastic cylinder = πR2H = 22/7 × (3.5)2 × 10 cm3 = 385 cm3

Difference in Capacity = (385 – 300)  = 85 cm3

Hence, the plastic cylinder has greater capacity.

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

Solution: 

Given that,

Radius of the base of a cylindrical pillar= 20 cm

The height of the cylindrical pillar = 10 m

Find how much concrete mixture would be required to build 14 such pillars

So

Volume of the cylindrical pillar = πR2H

= (22/7 × 202 × 1000) 



= 8800000/7 

= 8.8/7 m3                                        

The volume of 14 pillars = 8.8/7 × 14 = 17.6 m3

Hence, the volume of the 14 pillars = 17.6 m3

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 gm.

Solution: 

Given that,

The inner diameter of a cylindrical wooden pipe(d1) = 24 cm

So, the inner radius of a cylindrical pipe(r1) = 24/2 = 12 cm

The outer diameter of a cylindrical wooden pipe(d2) = 28 cm

So, the outer radius of a cylindrical pipe(r2) = 28/2 = 14 cm



Height of cylindrical pipe (h) = 35 cm

Find the mass of the pipe, if 1 cm3 of wood has a mass of 0.6 gm

So, 

The Mass of pipe = Volume x density

= π(r22 – r12)

= 22/7 x (142 − 122) x 35 = 5720 cm3

Mass of 1 cm3 wood = 0.6 gm                           

Mass of 5720 cm3 wood = 5720 × 0.6 = 3432 gm = 3.432 kg

Question 4. If the lateral surface of a cylinder is 94.2 cm2 and its height is 5 cm, find :

(i) the radius of its base

(ii) volume of the cylinder [Use pi = 3.141]

Solution : 

Given that,

The lateral surface of a cylinder = 94.2 cm2

The hight of the cylinder = 5cm

(i) Find the radius of its base

Let’s assume that the radius of cylinder be ‘r’

Curved surface of the cylinder = 2πrh 

94.2 = 2 (3.14)r(5)

r = 3 cm      

Hence, the radius of the cylinder is 3 cm                                           

(ii) As we know that 

The volume of the cylinder = πr2



= (3.14 × 32 × 5) 

= 141.3 cm3

Hence, the volume of the cylinder is 141.3 cm3  

Question 5. The capacity of a closed cylindrical vessel of height 1 m is 15.4 liters. How many square meters of the metal sheet would be needed to make it?

Solution: 

Given that,

The height of the cylindrical vessel = 1m

The capacity/volume of the cylinder = 15.4 liters = 0.0154 m3     (As we know 1m3 = 1000 liter)

Let’s assume that the radius of the circular ends of the cylinders be ‘r’

So the volume of the cylinder is 

V = πr2

0.0154 = (31.4)r2(1)

r = 0.07 m                                                           

Now we find the total surface area of a vessel:

TSA = 2πr(r + h)

= 2(3.14 x (0.07) x (0.07 + 1)) = 0.4703 m2

Hence, we need 0.4703 m2 of the metal sheet

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: 

Given that,

The diameter of cylindrical bowl = 7 cm = 3.5 cm      

So, the radius = 7/2 cm = 3.5 cm    



The bowl is filled with soup to a height =4cm

Now we find the volume soup in 1 bowl

V = πr2h

= 22/7 × 3.52 × 4 = 154 cm3

So the volume soup in 250 bowl

V = (250 × 154) = 38500 cm3 = 38.5 liter

Hence, the soup, hospital has to prepare daily to serve 250 patients is 38.5 liter.

Question 7. A hollow garden roller, 63 cm wide with a girth of 440 cm, is made of 4 cm thick iron. Find the volume of the iron.

Solution: 

Given that, 

Garden roller height = 63 cm,

Garden roller outer circumference = 440 cm,

Garden roller thickness = 4 cm

Find the volume of iron.

So, let’s assume that the R be the external radius and the inner radius be ‘r’

2πR = 440

2 x 22/7 x R = 440

R = 70

Now we find the value of inner radius:

r = R – 4

70 – 4 = 66cm

Now we find the volume of the iron:

V = π (R2 − r2) x h

= 22/7 x (702 − 662) x 63

= 22/7 x 4 x 136 x 63 = 107712 cm3

Hence, the volume of the iron is 107712 cm3

Question 8. A solid cylinder has a total surface area of 231cm2. Its curved surface area is 2/3 of the total surface area. Find the volume of the cylinder.

Solution: 

Given that,

Total surface area = 231cm2

Curved surface area = 2/3 x (Total Surface Area)

So, 

Curved surface area = 2/3 x 231 = 154

As we know that, 

the total surface area of cylinder = 2πrh + 2πr2 

2πrh + 2πr2 = 231 —————-(i)

Where, 2πrh is the curved surface area, So

154 + 2πr2 = 231

2πr2 = 231 – 154

2πr2 = 77

2 x 22/7 x r2 = 77

r2 = (7×7) / (2×2)



r = 7/2

The radius of cylinder = 7/2

Now we find the height of the cylinder

So, as we know that 

Curved surface area = 2πrh              

2πrh = 154

2 x 22/7 x 7/2 x h = 154

h = 154/22 = 7

So, the height of cylinder = 7

Now we find the volume of the cylinder:

Volume = πr2h

 = 22/7 x 7/2 x 7/2 x 7 = 269.5 cm3

So, the volume of the cylinder is 269.5 cm3

Question 9. The cost of painting the total outside surface of a closed cylindrical oil tank at 50 paise per square decimetre is Rs 198. The height of the tank is 6 times the radius of the base of the tank. Find the volume corrected to 2 decimal places.

Solution: 

Let’s assume that the radius of the tank = r dm

So, the height of the tank(h) = 6r dm

It is given that the cost of painting = 50 paisa per dm

So, the total cost of painting = Rs 198           

= 2πr(r + h) = 198

= 2 × 22/7 × r(r + 6r) × 1/2 = 198

 r = 3 dm

Hence the radius of the tank is 3 dm

Therefore, h = (6 × 3) dm = 18 dm

 As we know that, 

Volume of the tank = πr2

= 22/7 × 9 × 18 = 509.14 dm3

Question 10. The radii of two cylinders are in the ratio 2:3 and their heights are in the ratio 5:3. Calculate the ratio of their volumes and the ratio of their curved surfaces.

Solution: 

Given that the ratio of the radii of two cylinders = 2:3

The ratio of the heights two cylinders = 5:3

So, let’s assume that the radius of the two cylinders are 2x and 3x 

The height of the two cylinders is 5y and 3y

Find: The ratio of their volumes and the ratio of their curved surfaces

So, for the ratio of their volumes:

We have

Volume of cylinder A/ Volume of cylinder B = π (r)2 h/π (R)2

= π (2x)2 5y/π (3x)2 3y = 20/27      

Hence, the ratio of the volumes of two cylinders are 20:27.

So, for the ratio of their surface area:

We have                          

Surface area of cylinder A / Surface area of cylinder B = 2πrh/2πRH

= (2π × 2x × 5y) / (2π × 3x × 3y) = 10 / 9                      

Hence, the ratio of the surface area of two cylinders are 10:9.

Question 11. The ratio between the curved surface area and the total surface area of a right circular cylinder is 1 : 2. Find the volume of the cylinder, if its total surface area is 616 cm2.

Solution: 

Given that

Total surface area (TSA) = 616 cm2

The ratio between the curved surface area and the total surface area of a right circular cylinder = 1 : 2

Find: the volume of the cylinder

According to the question

Curved Surface Area / Total Surface Area = 1/2                           

CSA = 1/2 x TSA



CSA = 1/2 x 616

CSA = 308 cm2

Now, we find the total surface area 

TSA = 2πrh + 2πr2

616 = CSA + 2πr2

616 = 308 + 2πr2

2πr2 = 616 – 308

2πr2 = 308

πr2 = 308/2

r2 = 308/2π

r = 7 cm

Since, CSA = 308 cm2                              

2πrh = 308

2 x 22/7 x 7 x h = 308

h = 7cm

Now we find the volume of cylinder 

V = πr2 x h

= 22/7 x 7 x 7 x 7 

= 22 x 49 

= 1078 cm3

Hence, the volume of cylinder is 1078 cm3

Question 12. The curved surface area of a cylinder is 1320 cm2 and its base had diameter 21 cm. Find the height and volume of the cylinder.

Solution: 

Given that 

The curved surface area of a cylinder = 1320 cm

Diameter of its base = 21 cm

So, radius = 21/2 = 10.5 cm

r = 21/2 = 10.5 cm

Find: the height and volume of the cylinder.

So, the curved surface area of a cylinder is 

CSA = 2πrh 

2 x 22/7 x 10.5 x h = 1320

h = 1320/66 = 20 cm

So the height of the cylinder is 20 cm

Now we find the volume of cylinder 

V = πr2 h

= 22/7 x 10.5 x 10.5 x 20

= 22 x 1.5 x 10.5 x 20 = 6930 cm3

Hence, the volume of cylinder is 6930 cm3

Question 13. The ratio between the radius of the base and the height of a cylinder is 2:3. Find the total surface area of the cylinder, if its volume is 1617 cm3.

Solution: 

Given that, 

The volume of the cylinder = 1617 cm3

The ratio between the radius of the base and the height of a cylinder = 2:3

r/h = 2/3

r = 2/3 x h  ——————–(i)

Find: The total surface area of the cylinder

So, we find the volume of cylinder 

V = πr2 h

1617 = 22/7 x (2/3 x h)2 x h

1617 = 22/7 x (2/3 x h)3

h3 = (1617 x 7 x 3) / 22 x 4

h = 10.5 cm

From, eqn. (i), we get

r = 2/3 x 10.5 = 7 cm

Now we find the total surface area of cylinder 

TSA = 2πr (h + r)

= 2 x 22/7 x 7(10.5 + 7) 

= 44 x 17.5 

= 770 cm2

Hence, the total surface area of cylinder is 770 cm2

Question 14. A rectangular sheet of paper, 44 cm x 20 cm, is rolled along its length of form cylinder. Find the volume of the cylinder so formed.

Solution: 

Given that, 

The dimensions of the rectangular sheet of paper = 44 cm x 20 cm 

So, 

Length = 44 cm,

Height = 20 cm

Find: The volume of the cylinder 

Curved Surface Area = 2πr

2πr = 44

r = 44/2π

r = 44/2π = 7 cm



Hence, the radius of the cylinder is 7 cm

Now, we find the volume of cylinder 

V = πr2 h

= 22/7 x 7 x 7 x 20

= 154 x 20 = 3080 cm3

Volume of cylinder is 3080 cm3

Question 15. The curved surface area of the cylindrical pillar is 264 m2 and its volume is 924 m3. Find the diameter and the height of the pillar.

Solution: 

Given that,

The curved surface area of the cylindrical pillar = 264 m2

The volume of the cylindrical pillar = 924 m3

We have to find the diameter and the height of the pillar

So, 

Volume of the cylinder 

V = πr2h

π x r2 x h = 924

πrh(r) = 924

πrh = 924/r

As we know that the curved surface area of the cylinder

CSA = 2πrh 

 264 = 2πrh …(1)

Substitute πrh in this eq and we get,

2 x 924/r = 264

 r = 1848/264 = 7 m

Substitute r value in eq (i) and we get,

2 x 22/7 x 7 x h = 264

h = 264/44 = 6 m

Hence, the diameter = 2r = 2(7) = 14 m and height = 6 m

Question 16. Two circular cylinders of equal volumes have their heights in the ratio 1 : 2. Find the ratio of two radii.

Solution: 

Let’s assume that we have two cylinders,

So, the radius of the cylinders = r1, r2 

The height of the cylinders = h1, h2 

The volume of the cylinders = v1, v2 

According to the question 

It is given that the h1/h2 = 1/2 and v1 = v2     

We have to find the ratio of two radii

So, 

v1/v2 = (r1/r2)2 x (h1/h2)

As v1 = v2

v1/v1 = (r1/r2)2 x (1/2)

1 = (r1/r2)2 x (1/2)

(r1/r2)2 = (2/1)

(r1/r2) = √2 / 1

Hence, the ratio of the radii are √2:1




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