A cylinder has a height of 11 feet. Its volume is cubic feet. What is the radius of the
cylinder?

Question

A cylinder has a height of 11 feet. Its volume is $$ 9,982.06 $$ cubic feet. What is the radius of the cylinder?

UpStudy AI · Accepted Answer

To find the radius of the cylinder, we can use the formula for the volume of a cylinder:

$$
V = \pi r^2 h
$$

where $$ V $$ is the volume, $$ r $$ is the radius, and $$ h $$ is the height. We are given:

- $$ V = 9,982.06 $$ cubic feet
- $$ h = 11 $$ feet

We can rearrange the formula to solve for the radius $$ r $$:

$$
r^2 = \frac{V}{\pi h}
$$

Substituting the known values into the equation:

$$
r^2 = \frac{9,982.06}{\pi \times 11}
$$

Calculating $$ \pi \times 11 $$:

$$
\pi \approx 3.14159 \quad \Rightarrow \quad \pi \times 11 \approx 34.5575
$$

Now substituting this back into the equation for $$ r^2 $$:

$$
r^2 = \frac{9,982.06}{34.5575} \approx 289.56
$$

Next, we take the square root to find $$ r $$:

$$
r = \sqrt{289.56} \approx 17.0
$$

Thus, the radius of the cylinder is approximately:

$$
\boxed{17.0} \text{ feet}
$$
The radius of the cylinder is approximately 17.0 feet.

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