RD Sharma 2020 solution class 9 chapter 19 Surface Area and Volume of a Right Circular Cylinder MCQS

MCQS

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Question 1:

Mark the correct alternative in each of the following:

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

Answer 1:

Let S1 be the curved surface area of the cylinder with radius r1 and height h1, then

……. (1)

Now, let S2 be the surface area after changing the dimension, then

So,

Hence, the correct option is (c)

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

Answer 2:

Let V1 and V2 be the volume of the two cylinders with radius r1 and height h1, and radius r2 and height h2, where

So,

……. (1)

Now,

…… (2)

From equation (1) and (2), we have

Hence, the correct option is (c)

Question 3:

The number of surfaces in right cylinder is

(a) 1

(b) 2

(c) 3

(d) 4

Answer 3:

In a cylinder there are three surfaces, one is curved surface area and other two are circular discs.

Hence, the 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

Answer 4:

From the following figure of cylinder we observe that the vertical cross section is the rectangle PQRS.

Hence, the correct option is (b)

Question 5:

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

(a) 13πr2h

(b) πr2h

(c) 2πr (h + r)

(d) 2πrh

Answer 5:

It is given that r is the radius and h is the height of the cylinder.

We know that the volume of cylinder is given by the formula

Hence, the correct option is (b)

Question 6:

The number of surfaces of a hollow cylindrical object is

(a) 1

(b) 2

(c) 3

(d) 4

Answer 6:

In a hollow cylinder, there are two curved surface areas: inner and outer and one circular base with inner and outer surface area.

Hence, the correct option is (d)

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

Answer 7:

Let V1 be the volume of the cylinder with radius r1 and height h1, then

……. (1)

Now, let V2 be the volume after changing the dimension, then

So,

Hence, the 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

Answer 8:

Let V1 be the volume of the cylinder with radius r1 and height h1, then

……. (1)

Now, let V2 be the volume after changing the dimension, then

So,

Hence, the 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

Answer 9:

Let V1 be the volume of the cylinder with radius r1 and height h1, then

……. (1)

Now, let V2 be the volume after changing the dimension, then

So,

Hence, the correct option is (c)

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

(a) 2πh2

(b) 32πh2

(c) 43πh2

(d) πh2

Answer 10:

Let r be the radius of the cylinder and h be its height.

It is given that:

Therefore, total surface area S is:

Hence, the correct option is (b)

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) 40π

(b) 80π

(c) 160π

(d) 200π

Answer 11:

Let r be the radius of the cylinder and h be its height.

It is given that:

And,

Therefore, total surface area S of the sheet required is:

Hence, the correct option is (b)

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Question 12:

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

(a) 1 : 2

(b) 2:1

(c) 1 : 2

(d) 1 : 4

(d)

Answer 12:

Let V1 and V2 be the volume of the two cylinders with h1 and h2 as their heights:

Let r1 and r2 be their base radius.

It is given that


Hence, the correct option is (b)

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

Answer 13:

Let V1 and V2 be the volume of the two cylinders with h1 and h2 as their heights:

Let r1 and r2 be their base radius.

It is given that


Hence, the length will become 9 times.

Hence, the correct option is (c)

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?

(a) 4

(b) 12

(c) 2

(d) 12

Answer 14:

Let V1 be the volume of the cylinder with radius r1 and height h1, then

……. (1)

Now, let V2 be the volume after changing the dimension, then

So,

It is given that V1 =V2Therefpre,

Hence, the correct option is (b)

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?

(a) x22π

(b) x2π

(c) 2xπ

(d) π2x

Answer 15:

Let V1 be the volume of the cylinder with radius r and height h, then

……. (1)

Now, let V2 be the volume of the box, then

It is given that V1 =1/4 V2Therefpre,

Hence, the correct option is (b)

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?

Answer 16:

Let h be the height of the cylinder with radius r.

It is given that:

Therefore, the volume of the cylinder is

Hence, the correct option is (a)

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) 2πr (r+h)

(b) πr (r+2h)

(c) πr+(2r+h)

(d) 2πr2+h

Answer 17:

Let S be the total surface area of the closed cylinder with radius r and height h, then

Hence, the correct option is (a)

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?

(a) 24π

(b) 48π

(c) 32π

(d) 48π

Answer 18:

Let r be the radius of the cylinder. It is given that the height drops 3 inches, when 1 cubic foot of sand is poured out and 1 foot = 12 inch

So,

Hence, the correct option is (b)

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) v1a1=v2a2

Answer 19:

Let the radius of the base of the cylinders be r and R.
Now, let sheet with length a1 be used to form a cylinder with volume v1

So,
 2πr=a1r=a12π
Volume v1=πr2h=πa12π2a2=a12a24π
Similarly, 
let sheet with length a2 be used to form a cylinder with volume v2
So,

2πR=a2R=a22π
Volume v2=πR2h=πa22π2a1=a22a14π
Now,
 v1v2=a12a2a22a1=a1a2v1a2=v2a1
Hence, the correct option is (c).

 

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

(a) 23

(b) 12

(c) 32

(d) 2

Answer 20:

Let the original radius of the base of cylinder = rLet the original height of cylinder = hNow, original base area of the cylinder, S = πr2Now, original LSA of cylinder, A = 2πrh       ............1When the altitude is increased  to 6 times of its initial value and base area is decreased one-ninth of its initial value:Let the new height of the cylinder = h'Let the new radius of base of cylinder = r'Now, new base area of cylinder, S' = πr'2   Now, it is given that,new height of cylinder = 6×original height of cylinderh' = 6hAlso, new base area of cylinder = 19original base area of the cylinderS' = 19Sπr'2  = 19πr2r'2 = r32r' = r3Now, new LSA of cylinder, A' = 2πr'h'  A' = 2π × r3 × 6h = 2×2πrhA' = 2 A   Using 1Hence, lateral surface area of the cylinder becomes twice of the original.So, option d is correct.

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