Question

what is the surface area of the cylinder with height 7 cm and radius 4 cm? 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 $r = 4$ cm and $h = 7$ cm. First, calculate $2\pi r^2$: $2\pi(4)^2=2\pi\times16 = 32\pi$. Then calculate $2\pi rh$: $2\pi\times4\times7=56\pi$.

Step3: Add the two parts

$S=32\pi + 56\pi=88\pi$.

Step4: Calculate the numerical value

Using $\pi\approx3.14159$, $S = 88\times3.14159=276.46992$.

Step5: Round to the nearest thousandth

$S\approx276.470$.

Answer:

$276.470$