A sphere of maximum volume is cut out from a solid hemisphere of radius 7 cm. What is the ratio of the volume of the hemisphere to that of the cut out sphere?

Two cylindrical cans have equal base areas. If one of the can is 15 cm high and other is 20 cm high, find the ratio of their volumes.

Two cubes have their volumes in the ratio 1 : 27. Find the ratio of their surface areas.

The ratio of the volume of a cube to that of a sphere which will fit inside the cube is

A solid is hemispherical at the bottom and
conical (of same radius) above it. If the surface areas of the two parts are equal, then the ratio of its radius and the slant height of the conical part is

4 : 1

3 : 4

1 : 9

6 : π

1 : 2