Question

an outdoor swimming pool has a volume of 180π cubic feet and a height of 5 feet.
what is the diameter of the swimming pool?
d = \square ft.

Explanation:

Step1: Recall Cylinder Volume Formula

The volume \( V \) of a cylinder is given by \( V = \pi r^2 h \), where \( r \) is the radius and \( h \) is the height.

Step2: Substitute Known Values

We know \( V = 180\pi \) and \( h = 5 \). Substitute into the formula:
\( 180\pi = \pi r^2 \cdot 5 \)

Step3: Solve for \( r^2 \)

Divide both sides by \( 5\pi \):
\( \frac{180\pi}{5\pi} = r^2 \)
Simplify: \( 36 = r^2 \)

Step4: Find Radius \( r \)

Take the square root: \( r = \sqrt{36} = 6 \) feet.

Step5: Calculate Diameter \( d \)

Diameter \( d = 2r \), so \( d = 2 \cdot 6 = 12 \) feet.

Answer:

12