Question

a cylinder with a height of 5 m and a base radius of 2 m is shown. answer the parts below. make sure you use the correct units in your answers. if necessary, refer to the list of geometry formulas. (a) find the exact surface area of the cylinder. write your answer in terms of π. exact surface area: (b) using the aleks calculator, approximate the surface area of the cylinder. to do the approximation, use the π button on the calculator, and round your answer to the nearest hundredth. approximate surface area:

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. Given $r = 2$ m and $h = 5$ m.

Step2: Calculate the exact surface area

Substitute $r = 2$ and $h = 5$ into the formula:
\[

$$\begin{align*} S&=2\pi r^{2}+2\pi rh\\ &=2\pi(2)^{2}+2\pi(2)(5)\\ &=2\pi\times4 + 2\pi\times10\\ &=8\pi+20\pi\\ &=28\pi\text{ m}^2 \end{align*}$$

\]

Step3: Calculate the approximate surface area

Using $\pi\approx3.14159$, we have $S\approx28\times3.14159 = 87.96452\approx87.96\text{ m}^2$

Answer:

(a) $28\pi\text{ m}^2$
(b) $87.96\text{ m}^2$