Question
A triangular pyramid with a square base has a dotted line segment labeled h equals question mark extending from the top vertex to the base. The base of the pyramid is labeled a equals 13 feet 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)
Responses
4 ft.
4 ft.
12 ft.
12 ft.
10 ft.
10 ft.
225 ft.
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)
Responses
4 ft.
4 ft.
12 ft.
12 ft.
10 ft.
10 ft.
225 ft.
Answers
GPT-4o mini
To find the height (h) of a square-based pyramid given its volume (V) and the area of the base (A), you can use the formula for the volume of a pyramid:
\[
V = \frac{1}{3} A h
\]
Where:
- \( V \) is the volume of the pyramid,
- \( A \) is the area of the base,
- \( h \) is the height.
Given:
- \( V = 52 \) cubic feet
- \( A = 13 \) square feet
Now, we can plug these values into the formula and solve for \( h \):
\[
52 = \frac{1}{3} (13) h
\]
To eliminate the fraction, multiply both sides by 3:
\[
3 \times 52 = 13h
\]
\[
156 = 13h
\]
Now, divide both sides by 13 to solve for \( h \):
\[
h = \frac{156}{13}
\]
\[
h = 12 \text{ feet}
\]
Therefore, the height of Fatima’s pyramid is **12 ft.**
\[
V = \frac{1}{3} A h
\]
Where:
- \( V \) is the volume of the pyramid,
- \( A \) is the area of the base,
- \( h \) is the height.
Given:
- \( V = 52 \) cubic feet
- \( A = 13 \) square feet
Now, we can plug these values into the formula and solve for \( h \):
\[
52 = \frac{1}{3} (13) h
\]
To eliminate the fraction, multiply both sides by 3:
\[
3 \times 52 = 13h
\]
\[
156 = 13h
\]
Now, divide both sides by 13 to solve for \( h \):
\[
h = \frac{156}{13}
\]
\[
h = 12 \text{ feet}
\]
Therefore, the height of Fatima’s pyramid is **12 ft.**