Question

The volume of two spheres are in ratio 125 : 27 . find the differences of their surface areas in terms of π . the sum of the radii of the spheres is 8cm

Answer 1

Let the volume of spheres be v1 and v2 respectively
and raduis be r1 and r2
V1/V2=4/3πr1³/4/3πr2³
V1/V2=r1³/r2³
125/27=r1³/r2³
By taking cube root
5/3 =r1/r2
r1/r2=5/3
r1=5r2/3

r1+r2=8
5r2/3+r2=8
5r2+3r2/3=8
8r2=8×3
r2=24/8
r2=3

r1=5r2/3
r1=5×3/3
r1=15/3
r1=5

let surface area be A1 and A2

A1 = 4πr1²
A1 = 4×π×5×5
A1=100π cm²

A2 = 4πr2²
A2=4×π×3×3
A2=36π cm²
The differences of their surface areas=A1-A2
=100π-36π
=64πcm²