Class 9 Chapter 21 – Surface Area and Volume of A Sphere Exercise VSAQs solutions are provided here. This topic comes under analytical geometry and the formulas for the volume and the surface area of the sphere was first discovered by Archimedes. You will be seeing questions using these formulas and with regular practice yields fruitful results. Students can also download exercise VSAQs pdf for future reference by following the given link.
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Question 1: Find the surface area of a sphere of radius 14 cm.
Solution:
Radius of a sphere (r) = 14 cm
Surface area of a sphere = 4Ï€r2
= 4 × (22/7) × 142 cm2
= 2464 cm2
Question 2: Find the total surface area of a hemisphere of radius 10 cm.
Solution:
Radius of a hemisphere (r) = 10 cm
Total surface area of a hemisphere = 3Ï€r2
= 3 × (22/7) × 102 cm2
= 942 cm2
Question 3: Find the radius of a sphere whose surface area is 154 cm2.
Solution:
Surface area of a sphere = 154 cm2
We know, Surface area of a sphere = 4Ï€r2
So, 4Ï€r2 = 154
4 x 22/7 x r2 = 154
r2 = 49/4
or r = 7/2 = 3.5
Radius of a sphere is 3.5 cm.
Question 4: The hollow sphere, in which the circus motor cyclist 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 available to the motorcyclist for riding = Surface area of a sphere = 4Ï€r2
= 4 × (22/7) × 3.52 m2
= 154 m2
Question 5: Find the volume of a sphere whose surface area is 154 cm2.
Solution:
Surface area of a sphere = 154 cm2
We know, Surface area of a sphere = 4Ï€r2
So, 4Ï€r2 = 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, Volume of 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 is based problems to finding the volume and surface area of sphere using formulae. Below are some of the important formulas:
- Surface area of a sphere = 4Ï€r2
- Surface area of the hemisphere = 2Ï€r2
- surface area of solid hemisphere = 3Ï€r2
- Volume of a sphere = 4/3Ï€r3 Cubic Units
- Volume of hemisphere = 2/3 πr3
Where, r = radius of a sphere