Question

The volumes of two spheres are in the ratio 64 : 27. Find the difference of their surface areas, if the sum of their radii is 7 cm.

Answer 1

Let the radii of the two spheres be r₁ cm and r₂ cm respectively and their respective volumes be V₁ and V₂. Then,

Given, r₁ + r₂ = 7 ⇒ \(\frac43r^2+r^2\) = 7 ⇒ \(\frac{7r_2}{3}\) = 7 ⇒ r₂ = 3 cm.

∴ r₁ = \(\frac43\times3\) = 4 cm
∴ Difference in the surface areas of the two spheres = \(4πr^2_2-4πr^2_1\)

= \(4π(r^2_2-r^2_1)\) = 4 x \(\frac{22}{7}\times(16-9) =4\times\frac{22}{7}\times7\) cm² = 88 cm².