Question

If the radius of a sphere is increased by 3 cm. Its surface area is increased by 528 cm². The original radius of the sphere was? 
1. 5.5 cm
2. 5 cm
3. 6 cm
4. 6.5 cm

Answer 1

Correct Answer - Option 1 : 5.5 cm

GIVEN:

Increase in radius = 3 cm

Increase in surface area = 528 cm²

FORMULA USED:

Surface area of sphere = 4πr²

a² - b² = (a + b) (a - b)

CALCULATION:

Let original radius be r cm

∴ increased radius = (r + 3)cm

A.T.Q

4π(r + 3)² - 4πr² = 528 

4π{(r + 3)2 - r²} = 528

(r + 3 - r) (r + 3 + r) = (528/4) × (7/22)

(2r + 3) = 14

r = 11/2 = 5.5 cm

∴ The radius was 5.5 cm