On a trip to Egypt, Myra brought a small glass pyramid as a souvenir. Find the volume of the glass used to make the pyramid. Round to the nearest tenth. The base is 4 inches, heigh... On a trip to Egypt, Myra brought a small glass pyramid as a souvenir. Find the volume of the glass used to make the pyramid. Round to the nearest tenth. The base is 4 inches, height is 4 inches.
Understand the Problem
The question asks to calculate the volume of a square pyramid given the side length of the base and the height. We will use formula to solve this problem: Volume = (1/3) * base area * height.
Answer
$21.3 \text{ in}^3$
Answer for screen readers
$21.3 \text{ in}^3$
Steps to Solve
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Find the base area The base of the pyramid is a square with side length 4 inches. The area of a square is side * side. $$ \text{Base Area} = 4 \text{ in} \cdot 4 \text{ in} = 16 \text{ in}^2 $$
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Apply the volume formula The formula for the volume $V$ of a pyramid is: $$ V = \frac{1}{3} \cdot \text{Base Area} \cdot \text{Height} $$ We know that the height is 4 inches and the base area is 16 square inches, so we can substitute these values into the formula: $$ V = \frac{1}{3} \cdot 16 \text{ in}^2 \cdot 4 \text{ in} $$
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Calculate the volume $$ V = \frac{1}{3} \cdot 64 \text{ in}^3 = \frac{64}{3} \text{ in}^3 $$ $$ V \approx 21.333 \text{ in}^3 $$
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Round to the nearest tenth Rounding 21.333 to the nearest tenth gives 21.3.
$21.3 \text{ in}^3$
More Information
The volume of the glass used to make the pyramid is approximately $21.3 \text{ in}^3$.
Tips
A common mistake is forgetting to multiply by $\frac{1}{3}$ when calculating the volume of a pyramid. Another mistake is not squaring the side length when calculating the area of the square base. Also, the final answer needs to be rounded to the nearest tenth as requested in the problem statement.
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