Question

a cylinder has a radius of 4 feet. its volume is 653.12 cubic feet. what is the height of the cylinder?
round your answer to the nearest hundredth.
$h \approx \boldsymbol{\square}$ feet

Explanation:

Step1: Recall cylinder volume formula

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

Step2: Rearrange for height $h$

Isolate $h$ by dividing both sides by $\pi r^2$:
$$h = \frac{V}{\pi r^2}$$

Step3: Substitute given values

Substitute $V=653.12$, $r=4$, and use $\pi \approx 3.14$:
$$h = \frac{653.12}{3.14 \times 4^2} = \frac{653.12}{3.14 \times 16}$$

Step4: Calculate denominator first

$$3.14 \times 16 = 50.24$$

Step5: Compute final height

$$h = \frac{653.12}{50.24} = 13.00$$

Answer:

$h \approx 13.00$ feet