Question

numeric 1 point. a bucket can hold 12,308.8 cubic inches. the diameter of the bucket is 28 inches (in.). what is the height of the bucket? use 3.14 for π. round to the nearest hundredth if necessary. answer

Explanation:

Step1: Recall volume formula for cylinder

The volume formula for a cylinder is $V=\pi r^{2}h$, where $V$ is volume, $r$ is radius and $h$ is height. Given the diameter $d = 28$ inches, the radius $r=\frac{d}{2}=\frac{28}{2}=14$ inches and $V = 12308.8$ cubic - inches, $\pi=3.14$.

Step2: Rearrange formula to solve for height

We can rewrite the volume formula as $h=\frac{V}{\pi r^{2}}$.

Step3: Substitute values

Substitute $V = 12308.8$, $\pi = 3.14$ and $r = 14$ into the formula: $h=\frac{12308.8}{3.14\times14^{2}}$. First, calculate $14^{2}=196$, then $3.14\times196 = 615.44$. So $h=\frac{12308.8}{615.44}=20$.

Answer:

20