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