(Q8).A sphere, a cylinder and a cone have the same radius and same height. Find the ratio of their volumes.

[Hint : Diameter of the sphere is equal to the height of the cylinder and the cone.]

Answer:

The volume of a sphere is
4
3
 πr3

The volume of a cylinder is πr2h

The volume of a cone is
1
3
 πr2h
The ratio of their volumes would be
::

Given is that the height and radius of all three are equal

∴ height of sphere=diameter of sphere=×radius

Height of cone=height of cylinder=×radius

h=

Substituting in the above ratio

 : :
×
: :
= ::

=::

The ratio of volume of sphere, cylinder and cone would be ::