Question
The pyramid has a square base area of 13 ft squared. Fatima measures this square-based pyramid. She finds that its volume is 52 cubic feet. What is the height of Fatima’s pyramid?(1 point)Responses12 ft.12 ft.225 ft.225 ft.10 ft.10 ft.4 ft.
Answers
GPT-4o mini
The volume \( V \) of a square-based pyramid can be calculated using the formula:
\[
V = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]
Given that the base area is \( 13 \) square feet and the volume is \( 52 \) cubic feet, we can set up the equation:
\[
52 = \frac{1}{3} \times 13 \times h
\]
where \( h \) is the height of the pyramid. To solve for \( h \), we can first multiply both sides of the equation by \( 3 \):
\[
156 = 13 \times h
\]
Next, we can divide both sides by \( 13 \):
\[
h = \frac{156}{13} = 12 \text{ ft}
\]
Thus, the height of Fatima’s pyramid is \( \boxed{12} \) ft.
\[
V = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]
Given that the base area is \( 13 \) square feet and the volume is \( 52 \) cubic feet, we can set up the equation:
\[
52 = \frac{1}{3} \times 13 \times h
\]
where \( h \) is the height of the pyramid. To solve for \( h \), we can first multiply both sides of the equation by \( 3 \):
\[
156 = 13 \times h
\]
Next, we can divide both sides by \( 13 \):
\[
h = \frac{156}{13} = 12 \text{ ft}
\]
Thus, the height of Fatima’s pyramid is \( \boxed{12} \) ft.