Question

The volumes of two spheres A and B are in the ratio 1331 : 343. If the sum of radius of A and B is 36 cm then the surface area of B is.
1. 2500 cm²
2. 2546 cm²
3. 2646 cm²
4. 2464 cm²

Answer 1

Correct Answer - Option 4 : 2464 cm²

GIVEN:

Volume (A : B) = 1331 : 343

FORMULA USED:

Volume of sphere = 4/3 πr³

Surface area of sphere = 4πr²

CALCULATION:

Let the radius be r₁ and r₂

(4/3πr₁³)/(4/3πr₂³) = 1331/343

r₁³/r₂³ = 1331/343

r₁/r₂ = 11/7

A.T.Q

11 + 7 = 36 cm

18 ratio = 36 cm

∴ B's radius = 7 ratio = 14 cm

Surface area of B = 4 × 22/7 × 14 × 14 = 2464 cm²

∴ Surface area of B is 2464 cm²