Question

chapter 7 practice
lesson 5: drilling for understanding

1. find the height of the cylinder given the volume is 254 in³. round to the nearest inch.

we know

Explanation:

Step1: Find the radius

The diameter is 6 in, so the radius $r=\frac{6}{2}=3$ in.

Step2: Recall volume formula

The volume formula for a cylinder is $V = \pi r^{2}h$. We need to solve for $h$, so $h=\frac{V}{\pi r^{2}}$.

Step3: Substitute values

Substitute $V = 254$ in³ and $r = 3$ in into the formula for $h$. $h=\frac{254}{\pi\times3^{2}}=\frac{254}{9\pi}$.

Step4: Calculate and round

$h=\frac{254}{9\pi}\approx\frac{254}{9\times3.14}\approx\frac{254}{28.26}\approx9$ in.

Answer:

9 in