Question

YOU BE THE TEACHER Your friend finds the volume of the pyramid. Is your friend correct? Explain your reasoning.

Answer 1

Hint: Use the formula of the volume of the pyramid.

Step 1: The volume $V$ of the pyramid is one-third of product of the area of the base and the height of the prism.

Step 2: The formula of the volume of the pyramid is given by: $V=\frac{1}{3}Bh$

Where $B$ is the area of the base & $h$ is the height of the pyramid.

Area of the base, $B=w\times l$

Where $w$ is the width and $l$ is the length of the rectangular cross-section.

Step 3: Here, The height $h$ of the triangular pyramid is 7 inches.

$B=w\times l$

Width $w$ is 4 inches & the length is $l$ is 8 inches.

$B=\left(4\right)\left(8\right)$

Let’s substitute the values in the formula,

$$\begin{gathered} V=\frac{1}{3}Bh \\ =\frac{1}{3}\left(4\right)\left(8\right)\times 7 \\ =\frac{1}{3}\times 32\times 7 \\ =\frac{224}{3} \\ =74.67 \end{gathered}$$.

Your friend used the formula of the volume of the prism instead of the pyramid. But the given shape is pyramid.

So, Volume of the pyramid is given by $=\frac{1}{3}Bh$

In order to find the correct volume, We can also do the one-third of the final volume as the volume of the pyramid is one-third of the volume of the prism.

Hence, Your friend is not correct and the volume of the given pyramid is 74.67 cubic inches.