Question

1. a cylinder has volume $v = 486pi ft^3$. if the height is $h = 6 ft$ what is the diameter?

d = \boxed{} ft

Explanation:

Step1: Recall the volume formula for a cylinder

The volume \( V \) of a cylinder is given by the formula \( V=\pi r^{2}h \), where \( r \) is the radius and \( h \) is the height.
We know \( V = 486\pi\) cubic feet and \( h=6\) feet. Substitute these values into the formula:
\( 486\pi=\pi r^{2}\times6 \)

Step2: Solve for \( r^{2} \)

First, divide both sides of the equation by \( \pi \) (since \( \pi
eq0 \)):
\( \frac{486\pi}{\pi}=\frac{\pi r^{2}\times6}{\pi} \)
Simplifying, we get \( 486 = 6r^{2} \)
Then divide both sides by 6:
\( r^{2}=\frac{486}{6}=81 \)

Step3: Solve for \( r \)

Take the square root of both sides. Since \( r \) represents the radius (a non - negative quantity), we have:
\( r=\sqrt{81} = 9 \) feet

Step4: Find the diameter \( d \)

The diameter \( d \) of a circle is related to the radius \( r \) by the formula \( d = 2r \).
Substitute \( r = 9 \) into the formula:
\( d=2\times9=18 \) feet

Answer:

\( 18 \)