Questions: Calculate (2 pi r h+2 pi r^2) for the given values of (r) and (s).
(r=5.1)
(h=10.25)
(491.88 mathrm~mm^2)
(491.63 mathrm~mm^2)
(392.54 mathrm~mm^2)
(392.34 mathrm~mm^2)
Transcript text: Calculate $2 \pi r h+2 \pi r^{2}$ for the given values of $r$ and $s$.
\[
\begin{array}{l}
r=5.1 \\
h=10.25
\end{array}
\]
$491.88 \mathrm{~mm}^{2}$
$491.63 \mathrm{~mm}^{2}$
$392.54 \mathrm{~mm}^{2}$
$392.34 \mathrm{~mm}^{2}$
Solution
Solution Steps
To solve the problem, we need to calculate the surface area of a cylinder using the formula \(2 \pi r h + 2 \pi r^2\), where \(r\) is the radius and \(h\) is the height. We will substitute the given values of \(r = 5.1\) and \(h = 10.25\) into the formula and compute the result using Python.
Step 1: Identify the Formula
To find the surface area of a cylinder, we use the formula:
\[
A = 2 \pi r h + 2 \pi r^2
\]
where \( r \) is the radius and \( h \) is the height.
Step 2: Substitute the Given Values
Substitute the given values \( r = 5.1 \) and \( h = 10.25 \) into the formula:
\[
A = 2 \pi (5.1)(10.25) + 2 \pi (5.1)^2
\]