Question

an outdoor swimming pool has a volume of 245π 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 \( V = 245\pi \) and \( h = 5 \). Substitute into the formula:
\( 245\pi=\pi r^{2}(5) \)

Step3: Solve for \( r^{2} \)

Divide both sides by \( 5\pi \):
\( \frac{245\pi}{5\pi}=r^{2} \)
Simplify: \( 49 = r^{2} \)

Step4: Solve for \( r \)

Take the square root of both sides: \( r=\sqrt{49}=7 \) (radius is positive)

Step5: Find Diameter \( d \)

Diameter \( d = 2r \), so \( d = 2\times7 = 14 \)

Answer:

14