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

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.

TextbookNCERT
ClassClass 9
SubjectMaths
ChapterChapter 19
Chapter NameSurface Areas and Volume
of a Circular Cylinder
ExerciseMCQs

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 (r1) = r
and height (h1) = h
Surface area = 2πrh
If radius is doubled and height is halved
Surface Areas and Volume of a Circular Cylinder With Solutions PDF RD Sharma Class 9 Solutions
∴ 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 (r1) = 3x
and radius of second (r2) = x
and height of the first (h1) = y
and height of the second (h2) = 3y
Now volume of the first cylinder = πr2h
= π(3x)2 x y = 9πx2y
and of second cylinder = π(x2) (3y)
∴ Ratio between then = 9πx2y : 3πx2y
= 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
RD Sharma Class 9 Maths Book Questions Chapter 19 Surface Areas and Volume of a Circular Cylinder
Solution:
Volume of a cylinder = πr2h (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)2h = π x 4r2h
= 4πr2h = 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 = πr2h
If height is doubled and radius remain same, then volume = πr2(2h) = 2πr2h
∴ 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 = πr2h
If radius is halved and height is doubled
RD Sharma Mathematics Class 9 Solutions Chapter 19 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 Math Solution Class 9 Chapter 19 Surface Areas and Volume of a Circular Cylinder
Solution:
Let diameter of the base of a cylinder (r) = h
Then its height (h) = h
RD Sharma Class 9 Questions Chapter 19 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) 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
Maths RD Sharma Class 9 Chapter 19 Surface Areas and Volume of a Circular Cylinder
Solution:
Let r1 and h1 be the radius and height of the
first cylinder, then
Volume = πr12h1
Similarly r1 and h2 are the radius and height of the second cylinder
∴ Volume = πr2h2
But their volumes are equal,
RD Sharma Class 9 Chapter 19 Surface Areas and Volume of a Circular Cylinder MCQS

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 = πr2h1 …(i)
In second case, radius is decreased to one third
RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder
∴ 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?
RD Sharma Solutions Class 9 Chapter 19 Surface Areas and Volume of a Circular Cylinder
Solution:
Let r be the radius and h be the height then volume = πr2h
If height is doubled and volume is same and let x be radius then πr2h = π(x)2 x 2h
RD Sharma Class 9 PDF Chapter 19 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?
Surface Areas and Volume of a Circular Cylinder Class 9 RD Sharma Solutions
Solution:
Let r be the radius and h be the height, then volume = πr2h
This volume is 14 of the volume of a rectangular box
∴ Volume of box = 4πr2h
Let side of base of box = x and height h,
then volume = x2h
∴ 4πr2h = x2h
RD Sharma Class 9 Solution Chapter 19 Surface Areas and Volume of a Circular Cylinder
Class 9 RD Sharma Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder

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?
Class 9 Maths Chapter 19 Surface Areas and Volume of a Circular Cylinder RD Sharma Solutions
Solution:
In a cylinder,
h = circumference of the cylinder
RD Sharma Book Class 9 PDF Free Download Chapter 19 Surface Areas and Volume of a Circular 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) 2πr2 + 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?
RD Sharma Class 9 Book Chapter 19 Surface Areas and Volume of a Circular Cylinder
Solution:
Let h be the height and d be the diameter of a cylinder, then
Surface Areas and Volume of a Circular Cylinder With Solutions PDF RD Sharma Class 9 Solutions

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 vand height a2 and other having volume v2 and height a1. Then,
RD Sharma Class 9 Maths Book Questions Chapter 19 Surface Areas and Volume of a Circular Cylinder
Solution:
Length of each sheet = a1
and breadth = a2
Volume of cylinder = πr2h
In first case,
v1 is volume and a2 is the height
RD Sharma Mathematics Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder
RD Sharma Math Solution Class 9 Chapter 19 Surface Areas and Volume of a Circular Cylinder

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
RD Sharma Class 9 Questions Chapter 19 Surface Areas and Volume of a Circular Cylinder
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,
Maths RD Sharma Class 9 Chapter 19 Surface Areas and Volume of a Circular Cylinder MCQS

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