If the radius of a sphere is increased by 2 cm, its surface area increase by 704 cm2. What was the radius of the sphere before the increase? ( Use = )
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 13 cm.
New surface area = 4π(r + 2)2
Increase in surface area is given as 704 cm²
4π(r + 2)2 − 4πr2 = 704
4π[(r + 2)2 − r2] = 704
4π[(r2 + 4 + 4r) − r2] = 704
16π[(1 + r)] = 704
1 + r = (704 × 7)/(16 × 22)
1 + r = 14
r = 14 -1 = 13 cm