RD Sharma Solutions for Class 9 Chapter 21 Surface Area and Volume of a Sphere Exercise VSAQs are provided here. This topic comes under Analytical Geometry, and the formulas for the volume and the surface area of the sphere were first discovered by Archimedes. You will see solutions using these formulas, and with regular practice, you can achieve great results in the annual exam. Also, students can download the exercise VSAQs PDF for future reference by clicking on the following links.
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Access Answers to RD Sharma Solutions for Class 9 Maths Chapter 21 Surface Area and Volume of a Sphere Exercise VSAQs Page Number 21.25
Question 1: Find the surface area of a sphere of radius 14 cm.
Solution:
The radius of a sphere (r) = 14 cm
The surface area of a sphere = 4πr2
= 4 × (22/7) × 142 cm2
= 2464 cm2
Question 2: Find the total surface area of a hemisphere of radius 10 cm.
Solution:
The radius of a hemisphere (r) = 10 cm
The total surface area of a hemisphere = 3πr2
= 3 × (22/7) × 102 cm2
= 942 cm2
Question 3: Find the radius of a sphere whose surface area is 154 cm2.
Solution:
The surface area of a sphere = 154 cm2
We know, Surface area of a sphere = 4πr2
So, 4πr2 = 154
4 x 22/7 x r2 = 154
r2 = 49/4
or r = 7/2 = 3.5
The radius of a sphere is 3.5 cm.
Question 4: The hollow sphere, in which the circus motorcyclist performs his stunts, has a diameter of 7 m. Find the area available to the motorcyclist for riding.
Solution:
Diameter of hollow sphere = 7 m
So, radius of hollow sphere = 7/2 m = 3.5 cm
Now,
Area is available to the motorcyclist for riding = Surface area of a sphere = 4πr2
= 4 × (22/7) × 3.52 m2
= 154 m2
Question 5: Find the volume of a sphere whose surface area is 154 cm2.
Solution:
The surface area of a sphere = 154 cm2
We know, Surface area of a sphere = 4πr2
So, 4πr2 = 154
4 x 22/7 x r2 = 154
or r2 = 49/4
or r = 7/2 = 3.5
Radius (r) = 3.5 cm
Now,
Volume of sphere = 4/3 π r3
= (4/3) π × 3.53
= 179.66
Therefore, the volume of the sphere is 179.66 cm3.
RD Sharma Solutions for Class 9 Maths Chapter 21 Surface Area and Volume of a Sphere Exercise VSAQs
RD Sharma Solutions Class 9 Maths Chapter 21 Surface Area and Volume of a Sphere Exercise VSAQs are based on problems to find the volume and surface area of a sphere using formulae. Below are some of the important formulas:
- The surface area of a sphere = 4πr2
- The surface area of the hemisphere = 2πr2
- The surface area of a solid hemisphere = 3πr2
- The volume of a sphere = 4/3πr3 Cubic Units
- The volume of a hemisphere = 2/3 πr3
Where, r = radius of a sphere.
