Question

numeric 1 point a bucket can hold 3,061.5 cubic inches. the diameter of the bucket is 10 inches (in.). what is the height of the bucket? use 3.14 for π. round to the nearest hundredth if necessary. answer

Explanation:

Step1: Find the radius

The diameter $d = 10$ inches, so the radius $r=\frac{d}{2}=\frac{10}{2}=5$ inches.

Step2: Use the volume formula for a cylinder

The volume formula of a cylinder is $V=\pi r^{2}h$. We know $V = 3061.5$ cubic - inches, $\pi=3.14$ and $r = 5$ inches. Rearranging the formula for $h$ gives $h=\frac{V}{\pi r^{2}}$.

Step3: Substitute the values

Substitute $V = 3061.5$, $\pi=3.14$ and $r = 5$ into the formula for $h$: $h=\frac{3061.5}{3.14\times5^{2}}=\frac{3061.5}{3.14\times25}=\frac{3061.5}{78.5}$.

Step4: Calculate the height

$h=\frac{3061.5}{78.5}=39$ inches.

Answer:

39.00