Question

A​ cone-shaped paper water cup has a height of 12 cm and a radius of 6 cm. If the cup is filled with water to one-sixth its​ height, what portion of the volume of the cup is filled with​ water?

Answer 1

1/216

Explanation:

The ratio of volumes of similar shapes is the cube of the scale factor. The filled portion of the cone is similar to the entire cone.

Linear scale factor

If the filled height is 1/6 of the total height, the scale factor for linear dimensions is 1/6.

Volume scale factor

The scale factor for the volume is the cube of the scale factor for linear dimensions. it is ...

(1/6)³ = 1/216

The volume of the filled portion of the cup is 1/216 of the volume of the cup.