Chapter 12.3, Problem 8ST1

To determine

To find: the ratio of volume of prism and pyramid.

Answer to Problem 8ST1

The ratio of volume of prism and pyramid is $\frac{6}{5}$ .

Explanation of Solution

Given information:

Height of prism, $h_1=2\text{ m }$

Height of pyramid, $h_2=5\text{ m}$

Pyramid and prism have congruent bases.

Calculation:

Calculate the volume of prism and pyramid.

Volume of prism $=B{h}_1$   ...(1)

Volume of pyramid $=\frac{1}{3}B{h}_2$   ...(2)

Dividing equation (1) by (2):

  $\begin{array}{l}\frac{\text{Volume of prism}}{\text{Volume of pyramid}}=\frac{\sout{B}{h}_1}{\frac{1}{3}\sout{B}{h}_2}\\ =\frac{3h_1}{h_2}\\ =\frac{3\times 2}{5}\\ =\frac{6}{5}\end{array}$

Therefore, the ratio of volume of prism and pyramid is $\frac{6}{5}$ .