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)

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 $s$. \[ \begin{array}{l} r=5.1 \\ h=10.25 \end{array} \] $491.88 \mathrm{~mm}^{2}$ $491.63 \mathrm{~mm}^{2}$ $392.54 \mathrm{~mm}^{2}$ $392.34 \mathrm{~mm}^{2}$
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Solution

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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: \[ A = 2 \pi (5.1)(10.25) + 2 \pi (5.1)^2 \]

Step 3: Calculate Each Term

Calculate the lateral surface area: \[ 2 \pi (5.1)(10.25) = 2 \times 3.1416 \times 5.1 \times 10.25 \approx 328.8 \]

Calculate the area of the two bases: \[ 2 \pi (5.1)^2 = 2 \times 3.1416 \times 5.1^2 \approx 163.1 \]

Step 4: Sum the Areas

Add the lateral surface area and the area of the two bases to find the total surface area: \[ A = 328.8 + 163.1 = 491.9 \]

Final Answer

\(\boxed{491.88 \, \text{mm}^2}\)

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