Question

A sphere, a cylinder and a cone have the same diameter. The height of the cylinder and also the cone are equal to the diameter of the sphere. Find the ratio of their volumes.

Answer 1

In the given problem, we are given a cone, a sphere and a cylinder which have equal diameter. Also, the height of cylinder and cone is equal to the diameter of the sphere. We need to find the ratio of their volumes.

So,

Let the diameter of the cone, cylinder and sphere be x cm.

Now, the height of the cone and cylinder is equal to the diameter of the hemisphere. Therefore, the height of the cone and cylinder = x cm

Now, the next step is to find the volumes of each of these.

Volume of a cone (V₁) =

Volume of a sphere (V₂) =

Volume of a cylinder (V₃) =

So, now the ratio of their volumes = (V₂) : (V₃) : (V₁)

Therefore, the ratio of the volumes of the given sphere, cylinder and cone is.