Chapter 12.5, Problem 39HP

To determine

To determine an example of a pyramid and a prism that has the same base and the same volume.

Explanation of Solution

Given:

A pyramid and a prism

Formula used:

Volume of the pyramid $=\frac{lwh}{3}\left[l=\text{length, }w\text{=}\text{width, }h\text{=}\text{height}\right]$

Volume of the rectangular prism $=lwh\left[l=\text{length, }w\text{=}\text{width, }h\text{=}\text{height}\right]$

Let’ consider the base of the rectangular prism have dimensions $5\times 2$ and the height of $5$ unit.

  $\Rightarrow$ Volume of the rectangular prism $=lwh$

  $\Rightarrow$ Volume of the rectangular prism $=5\times 2\times 5$

  $\Rightarrow$ Volume of the rectangular prism $=5\times 2\times 5$

  $\Rightarrow$ Volume of the rectangular prism $=50{\text{unit}}^3$

Now consider,

The base of the pyramid has dimensions $5\times 2$ and the height of $15$ unit,

  $\Rightarrow$ Volume of the pyramid $=\frac{lwh}{3}$

  $\Rightarrow$ Volume of the pyramid $=\frac{5\times 2\times 15}{3}$

  $\Rightarrow$ Volume of the pyramid $=5\times 2\times 5$

  $\Rightarrow$ Volume of the pyramid $=50{\text{unit}}^3$

Conclusion:

Therefore, the following example of a pyramid and a prism has the same base and the same volume.