what is the surface area of this cylinder? round your answer to the nearest hundredth. 71 in 99 in square inches submit

Question

Accepted Answer

# Explanation:
## Step1: Recall the formula for the surface area of a cylinder
The formula for the surface area of a cylinder is $S = 2\pi r^{2}+2\pi rh$, where $r$ is the radius and $h$ is the height.
## Step2: Identify the values of $r$ and $h$
Given $r = 71$ in and $h=99$ in.
## Step3: Calculate the area of the two circular bases ($2\pi r^{2}$)
$$
\begin{align*}
2\pi r^{2}&=2\times\pi\times(71)^{2}\
&=2\times\pi\times5041\
& = 10082\pi
\end{align*}
$$
## Step4: Calculate the lateral surface area ($2\pi rh$)
$$
\begin{align*}
2\pi rh&=2\times\pi\times71\times99\
&=2\times\pi\times7029\
&=14058\pi
\end{align*}
$$
## Step5: Sum the two parts to get the total surface area
$$
\begin{align*}
S&=10082\pi + 14058\pi\
&=(10082 + 14058)\pi\
&=24140\pi
\end{align*}
$$
Substitute $\pi\approx3.14159265$
$$
\begin{align*}
S&=24140\times3.14159265\
&=24140\times3.14159265\
&=75837.04657
\end{align*}
$$

# Answer:
$75837.05$ square inches

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the formula for the surface area of a cylinder

Step2: Identify the values of \(r\) and \(h\)

Step3: Calculate the area of the two circular bases (\(2\pi r^{2}\))

Step4: Calculate the lateral surface area (\(2\pi rh\))

Step5: Sum the two parts to get the total surface area

Answer: