Question

A sphere, a cylinder and a cone have the same radius and same height. Find the ratio of their volumes. [Diameter of the sphere is equal to the heights of the cylinder and the cone.] A sphere, a cylinder and a cone have the same radius and same height.

Answer 1

Sphere Cylinder Cone 

Radius = r r r 

Height = r 2r = h 2r = h 

Now C.S.A of spehre = 4πr …………….(1) 

C.S.A of cylinder = 2πrh 

= 2πr.2r-2r = 4πr ……………….. (2) 

Now for cone, slant height = l

Then C.S.A of cone = πrl = πr. √5r = √5 πr² ……………. (3) 

∴ Ratio of C.S.A of sphere, cylinder and cone = 4πr² : 4πr² : √5 πr² 

= 4 : 4 : √5