QuestionFind the height of a tree stump modeled as a cylinder with radius 37 in and volume 77415 in³. Round to the nearest tenth.

Studdy Solution

STEP 1

Assumptions1. The tree stump is modeled as a right cylinder. The radius of the stump is37 inches3. The volume of the stump is77415 cubic inches4. We are asked to find the height of the stump5. The formula for the volume of a right cylinder is $V = \pi r^ h$ , where $V$ is the volume, $r$ is the radius, and $h$ is the height

STEP 2

We can rearrange the formula for the volume of a right cylinder to solve for the height.
$h = \frac{V}{\pi r^2}$

STEP 3

Now, plug in the given values for the volume and radius to calculate the height.
$h = \frac{77415}{\pi \times37^2}$

STEP 4

Calculate the square of the radius.
$37^2 =1369$ $h = \frac{77415}{\pi \times1369}$

STEP 5

Calculate the height of the stump.
$h = \frac{77415}{\pi \times1369} \approx17.8$ The height of the stump is approximately17.8 inches.

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