Question

what is the surface area of the cylinder with height 8 mi and radius 2 mi? round your answer to the nearest thousandth.

Explanation:

Step1: Recall surface - area formula

The surface - area formula of a cylinder is $S = 2\pi r^{2}+2\pi rh$, where $r$ is the radius and $h$ is the height.

Step2: Substitute given values

Given $r = 2$ mi and $h = 8$ mi. Substitute into the formula: $S=2\pi(2)^{2}+2\pi(2)(8)$.

Step3: Calculate each term

First term: $2\pi(2)^{2}=2\pi\times4 = 8\pi$. Second term: $2\pi(2)(8)=32\pi$.

Step4: Add the terms

$S=8\pi + 32\pi=40\pi$.

Step5: Approximate the value

Using $\pi\approx3.14159$, $S\approx40\times3.14159 = 125.6636$. Rounding to the nearest thousandth, $S\approx125.664$ $mi^{2}$.

Answer:

$125.664$