The sum of the surface of a sphere and a cube is given. Prove that the sum of their volumes is least when the diameter of the sphere is equal to the edge of the cube.

The sum of the cubes of 1st n natural numbers is

The sum of the total surface areas of a sphere and a cube is constant. Find the ratio of the radius of the sphere and the length of the edge of the cube so that the sum of their volumes is minimum.

The sum of the cubes of first n natural numbers is -

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 heights of the cylinder and the cone]

The sum of the areas of six surfaces of a cube is 216 sq-cm, find the volume of the cube.

If the diameter of a sphere be 6 cm, then the volume of the sphere will be

The volume of a solid sphere of diameter R is

The perimeter of one surface of a cube is 20cm. What is the volume of the cube?

The sum of radii of two spheres is 10 cm and the sum of their volume is 880 cm^3 . What will be the product of their radii?