In this chapter, we provide RD Sharma Solutions for Chapter 19 Surface Areas and Volume of a Circular Cylinder MCQs for English medium students, Which will very helpful for every student in their exams. Students can download the latest RD Sharma Solutions for Chapter 19 Surface Areas and Volume of a Circular Cylinder MCQs Maths pdf, free RD Sharma Solutions for Chapter 19 Surface Areas and Volume of a Circular Cylinder MCQs Maths book pdf download. Now you will get step by step solution to each question.

Textbook | NCERT |

Class | Class 9 |

Subject | Maths |

Chapter | Chapter 19 |

Chapter Name | Surface Areas and Volume of a Circular Cylinder |

Exercise | MCQs |

**RD Sharma Solutions for Class 9 Chapter 19 Surface Areas and Volume of a Circular Cylinder MCQs Download PDF**

Mark correct alternative in each of the following:

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:

Let radius of the first cylinder (r_{1}) = r

and height (h_{1}) = h

Surface area = 2πrh

If radius is doubled and height is halved

∴ Their surface area remain same (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

Solution:

Sol. Ratio in the diameters of two cylinder = 3:1

and ratio in their heights = 1:3

Let radius of the first cylinder (r_{1}) = 3x

and radius of second (r_{2}) = x

and height of the first (h_{1}) = y

and height of the second (h_{2}) = 3y

Now volume of the first cylinder = πr^{2}h

= π(3x)^{2} x y = 9πx^{2}y

and of second cylinder = π(x^{2}) (3y)

∴ Ratio between then = 9πx^{2}y : 3πx^{2}y

= 3 : 1 (c)

Question 3.

The number of surfaces in right cylinder is

(a) 1

(b) 2

(c) 3

(d) 4

Solution:

The number of surfaces of a right cylinder is three. (c)

Question 4.

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

(a) square

(b) rectangle

(c) rhombus

(d) trapezium

Solution:

The vertical cross-section of a right circular cylinder is always a rectangle. (b)

Question 5.

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

Solution:

Volume of a cylinder = πr^{2}h (b)

Question 6.

The number of surfaces of a hollow cylindrical object is

(a) 1

(b) 2

(c) 3

(d) 4

Solution:

The number of surfaces of a hollow cylindrical object is 4. (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

Solution:

If r be the radius and h be the height, then volume = πr2h

If radius is doubled and height remain same,

the volume will be

= π(2r)^{2}h = π x 4r^{2}h

= 4πr^{2}h = 4 x Volume

The volume is four times (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:

If r be the radius and h be the height, then volume of a cylinder = πr^{2}h

If height is doubled and radius remain same, then volume = πr^{2}(2h) = 2πr^{2}h

∴ Its doubled (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:

Let r be radius and h be height, then Volume = πr^{2}h

If radius is halved and height is doubled

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

Solution:

Let diameter of the base of a cylinder (r) = h

Then its height (h) = h

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 m^{2}, is

(a) 40π

(b) 80π

(c) 160π

(d) 200π

Solution:

Diameter of a cylindrical tunnel = 2 m

∴ Radius (r) = 22 = 1m

and length (h) = 40 m

Curved surfae area = 2πrh = 2 x π x 1 x 40 = 80π (b)

Question 12.

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

Solution:

Let r_{1} and h_{1} be the radius and height of the

first cylinder, then

Volume = πr_{1}^{2}h_{1}

Similarly r_{1} and h_{2} are the radius and height of the second cylinder

∴ Volume = πr^{2}h_{2}

But their volumes are equal,

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:

In the first case, r and h1, be the radius and height of the cylindrical wire

∴ Volume = πr^{2}h_{1} …(i)

In second case, radius is decreased to one third

∴ In second case height is 9 times (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?

Solution:

Let r be the radius and h be the height then volume = πr^{2}h

If height is doubled and volume is same and let x be radius then πr^{2}h = π(x)^{2} x 2h

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?

Solution:

Let r be the radius and h be the height, then volume = πr^{2}h

This volume is 14 of the volume of a rectangular box

∴ Volume of box = 4πr^{2}h

Let side of base of box = x and height h,

then volume = x^{2}h

∴ 4πr^{2}h = x^{2}h

Question 16.

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

Solution:

In a cylinder,

h = circumference of the cylinder

Question 17.

A cylinder with radius r and height ft 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) 2πr^{2} + h

Solution:

r is the radius of the base and ft is the height of a closed cylinder

Then total surface area = 2πr(r + h ) (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?

Solution:

Let h be the height and d be the diameter of a cylinder, then

Question 19.

Two steel sheets each of length a_{1} and breadth a_{2} are used to prepare the surfaces of two right circular cylinders – one having volume v_{1 }and height a_{2} and other having volume v_{2} and height a_{1}. Then,

Solution:

Length of each sheet = a_{1}

and breadth = a_{2}

Volume of cylinder = πr^{2}h

In first case,

v_{1} is volume and a_{2} is the height

Question 20.

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

Solution:

In first case,

Let r be the radius and h be the height of the cylinder. Then,

∴ Lateral surface area = 2πrh

In second case,

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