A solid sphere of radius R has a cylindrical hole of radius R/2 drilled through its center. The height of the cylinder removed is 2R (the full diameter). What is the ratio of the volume of the sphere to the volume of the removed cylinder?

Explanation

​Given: Sphere Radius = R R Cylinder Radius(r) = 2 ​ Cylinder Height(h) = 2R Solution: 4 3 Volume of Sphere = πR 3 ​ R 2 Volume of Cylinder = πr h = π ( ) (2R) 2 2 ​ R2 πR3 = π( ) (2R) = 4 2 ​ ​ Copyright © 2026 Adda247 4 4 Vol Sphere πR3 Ratio = = 13 3 ​ Vol Cylinder ​ ​ 2 πR ​ 4 2 8 = × = 3 1 3 ​ ​ Final Answer 8 : 3​