Question

In figure is shown a right circular cone of height 30 cm. A small cone is cut off from the top by a plane parallel to the base. If the volume of the small cone is 1/27 of the volume of given cone, find at what height above the base is the section made.​

Answer 1

20 cm

Explanation:

Think of a large cone, 30 cm high, and a small cone of x height.

The scale factor of a volume of the cube of the scale factor of linear dimensions.

The cubic root of 1/27 is 1/3.

This means that the height of the small cone is 1/3 the height of the large cone.

The large cone has height 30 cm.

The small cone has height 10 cm.

30 cm - 10 cm = 20 cm

Answer: 20 cm