area of sphere

Question

Had the diameter of a sphere been decreased by 2cm, its surface area would have diminished by 113.04 cm² . Find the surface area of the sphere.

Answer 1

The radius then decreases by 1 cm

 

4πR² - 4π(R - 1)² = 113.04

 

R² - R² + 2R - 1 = 113.04/(4π) = 8.9954

 

2R - 1 =  8.9954

 

R = (1+8.9954)/2 = 4.9977

 

The original surface area was

 

4πR² = 4π(4.9977) cm² = 62.803 cm²

Answer 2

The surface area of a sphere is

 

A = 4πr²

 

 

Write this in terms of diameter, d.

 

r = d / 2

 

 

A = 4π(d / 2)²

A = 4π(d² / 4)

A = πd²

 

 

We know that if we decrease the diameter, we also decrease the area.

 

A - 113.04 = (d - 2)² π

 

 

From this newly formed equation, add 113.04 on both sides of the equation to isolate A. 

 

A = (d - 2)² π + 113.04