Question

For a sphere of radius 6 cm, the numerical value of the surface area is how many percent of the numerical value of its volume?
1. 40%
2. 50%
3. 45%
4. 200%

Answer 1

Correct Answer - Option 2 : 50%

Given:

Radius of sphere, r = 6 cm

Concept used:

Surface area of sphere = 4πr²

Volume of sphere = (4/3)πr³

Calculation:

Surface area of sphere = 4πr²

⇒ (4π) × (6)²

⇒ 144π cm²

Volume of sphere = (4/3)πr³

⇒ [(4/3)π] × (6)³

⇒ 288π cm³

Required Percentage = [(Surface area of sphere)/(Volume of sphere)] × 100

⇒ (144π/288π) × 100

⇒ 100/2

⇒ 50%

∴ The required percentage is 50%.

Formula of Total Surface area of sphere and Curved Surface area of sphere is same that is 4πr².