When the radius of a sphere is increased by 5 cm, its surface area increased by 704 cm2, The diameter of the original sphere is ........(take π = 22/7)
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 6.2 cm
| Understanding | Application |
| Tricks |
In initial The surface area of the sphere = 4πr2 After increment 4π(r + 5)2 = 4π(r2 + 25 + 10r) |
| Now |
4π(r2 + 25 + 10r) - 4πr2 = 704 ⇒ 4πr2 + 100π + 40πr - 4πr2 = 704 ⇒ 20π(5 + 2r) = 704 ⇒ 5 + 2r = 704/20 × 7/22 ⇒ 5 + 2r = 224/20 ⇒ 2r = 224/20 - 5 ⇒ 2r = 124/20 |
| Hence |
r = 62/20 = 3.1 So diameter = 3.1 × 2 = 6.2 |