Question
The area of a square-based pyramid is 50 square yards. The volume of the pyramid is 250 cubic yards. What is the height of the pyramid?
Answers
GPT-4o mini
To find the height of the square-based pyramid, we first need to recall the formulas for the volume \( V \) and the area \( A \) of a square-based pyramid.
The volume \( V \) of a pyramid is given by the formula:
\[
V = \frac{1}{3} A_b h
\]
where \( A_b \) is the area of the base and \( h \) is the height of the pyramid.
For a square base, the area \( A_b \) is given in the problem as 50 square yards. Hence, we can write:
\[
V = \frac{1}{3} \cdot 50 \cdot h
\]
Given that the volume \( V \) is 250 cubic yards, we can set up the equation:
\[
250 = \frac{1}{3} \cdot 50 \cdot h
\]
To solve for \( h \), we first multiply both sides of the equation by 3 to eliminate the fraction:
\[
750 = 50h
\]
Next, we divide both sides by 50:
\[
h = \frac{750}{50} = 15
\]
Thus, the height of the pyramid is:
\[
\boxed{15} \text{ yards}
\]
The volume \( V \) of a pyramid is given by the formula:
\[
V = \frac{1}{3} A_b h
\]
where \( A_b \) is the area of the base and \( h \) is the height of the pyramid.
For a square base, the area \( A_b \) is given in the problem as 50 square yards. Hence, we can write:
\[
V = \frac{1}{3} \cdot 50 \cdot h
\]
Given that the volume \( V \) is 250 cubic yards, we can set up the equation:
\[
250 = \frac{1}{3} \cdot 50 \cdot h
\]
To solve for \( h \), we first multiply both sides of the equation by 3 to eliminate the fraction:
\[
750 = 50h
\]
Next, we divide both sides by 50:
\[
h = \frac{750}{50} = 15
\]
Thus, the height of the pyramid is:
\[
\boxed{15} \text{ yards}
\]