The sum of surface areas of a sphere and a cuboid with sides `x/3,x` and `2x` , is constant. Show that the sum of their volumes is minimum if `x` is equal to three times the radius of sphere.

The sum of the surface areas of a cuboid with sides x ,2x and x/3 and a sphere is given to be constant. Prove that the sum of their volumes is minimum, if x is equal to three times the radius of sphere. Also find the minimum value of the sum of their volumes.

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

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

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

The surface area of a sphere is 616\ c m^2 . Find its radius.

The surface area of a sphere is 2464 cm^(2), find its volume.

The surface area of a sphere is 100pi cm^(2) . Find its volume.

The sum of the perimeters of a square and a circle is given. Show that the sum of their areas is minimum when the length of a side of the square is equal to the diameter of the circle.

If the surface area of a sphere is 616 cm^(2), find its volume.

Find the volume and surface area of a sphere of radius 21 cm.