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Question

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

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Solution

## 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, $B=w×l$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.$B=w×l$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,$V=\frac{1}{3}Bh\phantom{\rule{0ex}{0ex}}=\frac{1}{3}\left(4\right)\left(8\right)×7\phantom{\rule{0ex}{0ex}}=\frac{1}{3}×32×7\phantom{\rule{0ex}{0ex}}=\frac{224}{3}\phantom{\rule{0ex}{0ex}}=74.67$.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.

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