Question

A square has its side equal to the radius of the sphere. The square revolves round a side to generate a surface of total area S. If A be the surface area of the sphere, which one of the following is correct ? 

(a) A = 3S 

(b) A = 2S 

(c) A = S 

(d) A < S

Answer 1

Let side of the square = a units. Then, radius of the sphere = a units 

Surface area of sphere (A) = 4πa² 

Since the square revolves round one of its sides, a right circular cylinder is generated whose height and radius are a units and a units respectively. So, 

Total surface area of the cylinder (S) = 2πr (r + h) = 2πa(a + a) = 4πa² 

∴ A = S.