Question
Fatima measures this square-based pyramid. She finds that its volume is 52 cubic feet. What is the height of Fatima’s pyramid? A = 13 ft.^2 (1 point) Responses 4 ft. 4 ft. 12 ft. 12 ft. 225 ft. 225 ft. 10 ft. 10 ft.
Answers
Answered by
GPT-4o mini
To find the height of the square-based pyramid, we can use the formula for the volume of a pyramid:
\[
V = \frac{1}{3} A h
\]
Where:
- \(V\) is the volume,
- \(A\) is the area of the base,
- \(h\) is the height.
In this case, we know:
- \(V = 52\) cubic feet,
- \(A = 13\) square feet.
We can rearrange the formula to solve for the height (\(h\)):
\[
h = \frac{3V}{A}
\]
Now, plug in the values for \(V\) and \(A\):
\[
h = \frac{3 \times 52}{13}
\]
Calculating this gives:
\[
h = \frac{156}{13} = 12
\]
Therefore, the height of Fatima's pyramid is \(12\) feet.
\[
V = \frac{1}{3} A h
\]
Where:
- \(V\) is the volume,
- \(A\) is the area of the base,
- \(h\) is the height.
In this case, we know:
- \(V = 52\) cubic feet,
- \(A = 13\) square feet.
We can rearrange the formula to solve for the height (\(h\)):
\[
h = \frac{3V}{A}
\]
Now, plug in the values for \(V\) and \(A\):
\[
h = \frac{3 \times 52}{13}
\]
Calculating this gives:
\[
h = \frac{156}{13} = 12
\]
Therefore, the height of Fatima's pyramid is \(12\) feet.