Find the volume of a sphere whose surface area is 154 cm².

Solution:

Since the surface area of the sphere is given, we can obtain the radius easily using the formula of the surface area of the sphere.

Let the radius of the sphere be r.

Surface area of the sphere = 4πr²

Volume of a sphere = 4/3πr³

Now, Surface area of the sphere = 4πr² = 154cm²

r² = 154cm² / 4π

r² = (154 cm²) ÷ (4 × 22/7)

r = √49/4cm²

r = 7/2 cm

Now, radius of the sphere = 7/2 cm

Therefore, volume of the sphere = 4/3πr³

= 4/3 × 22/7 × 7/2 cm × 7/2 cm × 7/2 cm

= 539/3 cm³

Therefore, volume of the sphere is 539/3 cm³.

☛ Check: NCERT Solutions for Class 9 Maths Chapter 13

Video Solution:

Find the volume of a sphere whose surface area is 154 cm².

NCERT Solutions for Class 9 Maths Chapter 13 Exercise 13.8 Question 7

Summary:

The volume of a sphere whose surface area is 154 cm² is equal to 539/3 cm³.

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