Question

The volume of this cylinder is 5,837.26 cubic inches. What is the radius?

Use ​𝜋 ≈ 3.14 and round your answer to the nearest hundredth.

r
11 in

r ≈
inches

Answer 1

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 of the cylinder.

Given:
- \( V = 5,837.26 \) cubic inches,
- \( \pi \approx 3.14 \),
- and \( h = 11 \) inches.

We need to find the radius \( r \). Rearranging the formula for volume to solve for \( r \):

\[
r^2 = \frac{V}{\pi h}
\]

Now substitute the known values:

\[
r^2 = \frac{5,837.26}{3.14 \times 11}
\]

Calculating the denominator:

\[
3.14 \times 11 = 34.54
\]

Now substituting this back into the formula:

\[
r^2 = \frac{5,837.26}{34.54} \approx 169.54
\]

Next, take the square root to find \( r \):

\[
r \approx \sqrt{169.54} \approx 13.03
\]

So, the radius \( r \) rounded to the nearest hundredth is:

\[
r \approx 13.03 \text{ inches}
\]