find the surface area of each figure. complete parts (a) through (e) below.
the surface area of the cube is 384 cm²
(simplify your answer. type an exact answer, using π as needed. type an exact answer, using π as needed)
b. right circular cylinder
the surface area of the right circular cylinder is
(simplify your answer. type an exact answer, using radi as needed. type an exact answer, using π as needed)

Question

Accepted Answer

# Explanation:
## Step1: Recall the formula for the surface area of a cylinder
The surface area formula of a right - circular cylinder is $S = 2\pi r^{2}+2\pi rh$, where $r$ is the radius of the base and $h$ is the height of the cylinder.
## Step2: Identify the values of $r$ and $h$
Given $r = 8\space cm$ and $h=16\space cm$.
## Step3: Calculate $2\pi r^{2}$
Substitute $r = 8$ into $2\pi r^{2}$:
$$
\begin{align*}
2\pi r^{2}&=2\pi\times(8)^{2}\
&=2\pi\times64\
& = 128\pi
\end{align*}
$$
## Step4: Calculate $2\pi rh$
Substitute $r = 8$ and $h = 16$ into $2\pi rh$:
$$
\begin{align*}
2\pi rh&=2\pi\times8\times16\
&=256\pi
\end{align*}
$$
## Step5: Calculate the surface area $S$
$$
\begin{align*}
S&=2\pi r^{2}+2\pi rh\
&=128\pi + 256\pi\
&=384\pi
\end{align*}
$$

# Answer:
$384\pi\space cm^{2}$

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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 \(2\pi r^{2}\)

Step4: Calculate \(2\pi rh\)

Step5: Calculate the surface area \(S\)

Answer: