Chapter E, Problem 12.3EX

To determine

To find the ratio of the volumes of the two similar cones.

Answer to Problem 12.3EX

Option (a)

Explanation of Solution

Given information: The height of two similar cones is 5 and 20 units.

Concept used:

Two cones are said to be similar, if their volumes are in the proportion as,

  $\frac{{\text{V}}_{\text{1}}}{{\text{V}}_{\text{2}}}\text{=}{k}^3={\left(\frac{a}{b}\right)}^3$

The radius and the height of the similar cones are in proportion,

  $\frac{{\text{V}}_{\text{1}}}{{\text{V}}_{\text{2}}}\text{=}{k}^3={\left(\frac{5}{20}\right)}^3={\left(\frac{1}{4}\right)}^3=\frac{1}{64}$

Hence, the ratios of the volumes of the similar cones are 1: 64.