Question

the volume of this cylinder is 3,818.24 cubic inches. what is the radius? round your answer to the nearest hundredth. 19 in r ≈ inches

Explanation:

Step1: Recall cylinder volume formula

The volume $V$ of a cylinder is $V = \pi r^2 h$, where $r$ is radius, $h$ is height.

Step2: Plug in known values

Substitute $V=3818.24$, $h=19$, $\pi\approx3.1416$:
$$3818.24 = 3.1416 \times r^2 \times 19$$

Step3: Isolate $r^2$ term

First calculate $3.1416 \times 19 \approx 59.6904$, then:
$$r^2 = \frac{3818.24}{59.6904} \approx 63.967$$

Step4: Solve for $r$

Take square root of both sides:
$$r = \sqrt{63.967} \approx 7.998$$

Step5: Round to nearest hundredth

Round $7.998$ to two decimal places.

Answer:

$r \approx 8.00$ inches