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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=13Bh

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=(4)(8)

Let’s substitute the values in the formula,

V=13Bh=13(4)(8)×7=13×32×7=2243=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 =13Bh

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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