RD Sharma Class 9 Solutions Chapter 21 Surface Areas and Volume of a Sphere MCQs

In this chapter, we provide RD Sharma Solutions for Chapter 21 Surface Areas and Volume of a Sphere 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 21 Surface Areas and Volume of a Sphere MCQs Maths pdf, free RD Sharma Solutions for Chapter 21 Surface Areas and Volume of a Sphere MCQs Maths book pdf download. Now you will get step by step solution to each question.

TextbookNCERT
ClassClass 9
SubjectMaths
ChapterChapter 21
Chapter NameSurface Area and volume of A Sphere
ExerciseMCQs

RD Sharma Solutions for Class 9 Chapter 21 Surface Areas and Volume of a Sphere MCQs

Question 1.
In a sphere, the number of faces is
(a) 1
(b) 2
(c) 3
(d) 4
Solution:
Number of faces of a sphere is 1 (a)

Question 2.
The total surface area of a hemisphere of radius r is
(a) πr2
(b) 2πr2
(c) 3πr2
(d) 4πr2
Solution:
Total surface area of a hemisphere is 37πr2 (c)

Question 3.
The ratio of the total surface area of a sphere and a hemisphere of same radius is
(a) 2 : 1
(b) 3 : 2
(c) 4 : 1
(d) 4 : 3
Solution:
Total surface area of a sphere = 4πr2
and total surface area of a hemisphere = 3m2
∴ Ratio 4πr2: 3πr2
= 4 : 3 (d)

Question 4.
A sphere and a cube are of the same height. The ratio of their volumes is
(a) 3 :4
(b) 21 : 11
(c) 4 : 3
(d) 11 : 21
Solution:
Let r be the height of a sphere and cube
RD Sharma Solutions Class 9 Chapter 21 Surface Areas and Volume of a Sphere MCQS

Question 5.
The largest sphere is cut off from a cube of side 6 cm. The volume of the sphere will be
(a) 27π cm3
(b) 36π cm3
(c) 108π cm3
(d) 12π cm3
Solution:
Side of cube = 6 cm
∴ Diameter of sphere cut off from it = 6 cm
RD Sharma Class 9 PDF Chapter 21 Surface Areas and Volume of a Sphere

Question 6.
A cylmderical rod whose height is 8 times of its radius is melted and recast into spherical balls of same radius. The number of balls will be
(a) 4
(b) 3
(c) 6
(d) 8
Solution:
Let r be the radius of a cylindrical rod = r
Then its height (h) = 8r
Volume = πr2h = πr2 x 8r = 8πr3
Radius of spherical ball = r
Surface Areas and Volume of a Sphere Class 9 RD Sharma Solutions

Question 7.
If the ratio of volumes of two spheres is 1 : 8, then the ratio of their surface areas is
(a) 1 : 2
(b) 1 : 4
(c) 1 : 8
(d) 1 : 16
Solution:
Let r1 and r2 be the radius of two spheres
RD Sharma Class 9 Solution Chapter 21 Surface Areas and Volume of a Sphere
Class 9 RD Sharma Solutions Chapter 21 Surface Areas and Volume of a Sphere

Question 8.
If the surface area of a sphere is 144π m2 then its volume (in. m3) is
(a) 288π
(b) 316π
(c) 300π
(d) 188π
Solution:
Surface area of a sphere = 144π m2
Let r be the radius, then
4πr2 = 144π
Class 9 Maths Chapter 21 Surface Areas and Volume of a Sphere RD Sharma Solutions

Question 9.
If a solid sphere of radius 10 cm is moulded into 8 spherical solid balls of equal radius, then the surface area of each ball (in sq. cm) is
(a) 100π
(b) 75π
(c) 60π
(d) 50π
Solution:
Radius of a sphere (r) = 10 cm
RD Sharma Book Class 9 PDF Free Download Chapter 21 Surface Areas and Volume of a Sphere
RD Sharma Class 9 Book Chapter 21 Surface Areas and Volume of a Sphere

Question 10.
If a sphere is inscribed in a cube, then the ratio of the volume of the sphere to the volume of the cube is
(a) π : 2
(b) π : 3
(c) π : 4
(d) π : 6
Solution:
Let side of a cube = a
Then volume of cube = a3
The diameter of inscribed sphere = a
Surface Areas and Volume of a Sphere With Solutions PDF RD Sharma Class 9 Solutions

Question 11.
If a solid sphere of radius r is melted and cast into the shape of a solid cone of height r, then the radius of the base of the cone is
(a) 2r
(b) 3r
(c) r
(d) 4r
Solution:
Radius of a sphere = r
RD Sharma Class 9 Maths Book Questions Chapter 21 Surface Areas and Volume of a Sphere
RD Sharma Mathematics Class 9 Solutions Chapter 21 Surface Areas and Volume of a Sphere

Question 12.
A sphere is placed inside a right circular cylinder so as to touch the top, base and lateral surface of the cylinder. If the radius of the sphere is r, then the volume of the cylinder is
RD Sharma Math Solution Class 9 Chapter 21 Surface Areas and Volume of a Sphere
Solution:
Radius of sphere = r
RD Sharma Class 9 Questions Chapter 21 Surface Areas and Volume of a Sphere

Question 13.
The ratio between the volume of a sphere and volume of a circumscribing right circular cylinder is
(a) 2 : 1
(b) 1 : 1
(c) 2 : 3
(d) 1 : 2
Solution:
Let r be the radius of the sphere, then 4
Volume = 43πr3
Diameter of circumscribed cylinder = 2r
∴ Radius = r
and height (h) = 2r
Maths RD Sharma Class 9 Chapter 21 Surface Areas and Volume of a Sphere

Question 14.
A cone and a hemisphere have equal bases and equal volumes the ratio of their heights is
(a) 1 : 2
(b) 2 : 1
(c) 4 : 1
(d) 2–√ : 1
Solution:
Let radius of hemisphere and a cone be r
RD Sharma Class 9 Chapter 21 Surface Areas and Volume of a Sphere

Question 15.
A cone, a hemisphere and a cylinder stand on equal bases and have the same height. The ratio of their volumes is
(a) 1 : 2 : 3
(b) 2 : 1 : 3
(c) 2 : 3 : 1
(d) 3 : 2 : 1
Solution:
∵ Bases of a cone, hemisphere and a cylinder are same
Let radius of each = r
and height of each = r
RD Sharma Class 9 Solutions Chapter 21 Surface Areas and Volume of a Sphere
RD Sharma Solutions Class 9 Chapter 21 Surface Areas and Volume of a Sphere

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