Question

b. a cylinder has a volume of 726 cubic inches and a radius of 8 inches. what is the height of the cylinder rounded to the nearest inch?

Explanation:

Step1: Recall volume formula

The volume formula for a cylinder is $V=\pi r^{2}h$, where $V$ is volume, $r$ is radius and $h$ is height.

Step2: Rearrange formula for height

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

Step3: Substitute given values

Given $V = 726$ cubic - inches and $r = 8$ inches. Substitute into the formula: $h=\frac{726}{\pi\times8^{2}}$.
First, calculate $8^{2}=64$. Then $h=\frac{726}{\pi\times64}$.
Since $\pi\approx3.14$, we have $h=\frac{726}{3.14\times64}=\frac{726}{200.96}\approx3.61$.

Step4: Round to nearest inch

Rounding $3.61$ to the nearest inch gives $4$ inches.

Answer:

4 inches