Question

A cylinder whose height is two-third of its diameter, has the same volume as that of a sphere of radius 4 cm. Find the radius of base of the cylinder.

Answer 1

Given radius of sphere R = 4 cm

Height of cylinder r = (2/3) d = 4 r/3 ; where r = radius of cylinder.

Also mentioned that volume of cylinder = volume of sphere -----(A)  

volume of cylinder = π r² h = π r² (4r/3) = π(4r³/3)

Volume of sphere = (4/3)πR³

According to statement A,

π(4r³/3) =(4/3)πR³  

r³ = 4³

r = 4 cm