Q20. - Geometry

Question

A pyramid and a prism both have height 8.2 cm and congruent hexagonal bases with area 22.3 cm². Give the ratio of their volumes.

Step-by-Step Solution

Answer

The ratio of volumes of pyramid and prism is$\frac{1}{3}:1$ .

Step 1. Given information.

Pyramid and prism height is 8.2 cm and congruent hexagonal bases with area 22.3 cm².

Step 2. Determine the ratio.

to find the ration of the volumes, divide the volumes of pyramid and prism,

Thus, the ratio of volumes of pyramid and prism is .$\begin{array}{l}\frac{v_{py}}{v_{pr}}=\frac{\frac{1}{3}bh}{bh}\\ \frac{v_{py}}{v_{pr}}=\frac{\frac{1}{3}\left(22.3\right)\left(8.2\right)}{\left(22.3\right)\left(8.2\right)}\text{ [substitute]}\\ \frac{v_{py}}{v_{pr}}=\frac{\frac{1}{3}}{1}\text{ [divide out common factor]}\end{array}$

Thus, the ratio of volumes of pyramid and prism is$\frac{1}{3}:1$ .