Pre-Algebra Examples

 $\begin{array}{r} h = & \frac{3}{2} \\ r = & \frac{13}{6} \end{array}$

Step 1

The surface area of a cylinder is equal to the sum of the areas of the bases each having an area of $π \cdot r^{2}$ , plus the area of the side. The area of the side is equal to the area of a rectangle with length $2 π r$ (the circumference of the base) times the height.

$2 π \cdot {(r a d i u s)}^{2} + 2 π \cdot (r a d i u s) \cdot (h e i g h t)$

Step 2

Substitute the values of the radius $r = \frac{13}{6}$ and height $h = \frac{3}{2}$ into the formula. Pi $π$ is approximately equal to $3.14$ .

$2 (π) {(\frac{13}{6})}^{2} + 2 (π) (\frac{13}{6}) (\frac{3}{2})$

Step 3

Simplify each term.

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Step 3.1

Apply the product rule to $\frac{13}{6}$ .

$2 π \frac{13^{2}}{6^{2}} + 2 (π) (\frac{13}{6}) (\frac{3}{2})$

Step 3.2

Raise $13$ to the power of $2$ .

$2 π \frac{169}{6^{2}} + 2 (π) (\frac{13}{6}) (\frac{3}{2})$

Step 3.3

Raise $6$ to the power of $2$ .

$2 π \frac{169}{36} + 2 (π) (\frac{13}{6}) (\frac{3}{2})$

Step 3.4

Cancel the common factor of $2$ .

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Step 3.4.1

Factor $2$ out of $2 π$ .

$2 (π) \frac{169}{36} + 2 (π) (\frac{13}{6}) (\frac{3}{2})$

Step 3.4.2

Factor $2$ out of $36$ .

$2 (π) \frac{169}{2 (18)} + 2 (π) (\frac{13}{6}) (\frac{3}{2})$

Step 3.4.3

Cancel the common factor.

$2 π \frac{169}{2 \cdot 18} + 2 (π) (\frac{13}{6}) (\frac{3}{2})$

Step 3.4.4

Rewrite the expression.

$π \frac{169}{18} + 2 (π) (\frac{13}{6}) (\frac{3}{2})$

Step 3.5

Combine $π$ and $\frac{169}{18}$ .

$\frac{π \cdot 169}{18} + 2 (π) (\frac{13}{6}) (\frac{3}{2})$

Step 3.6

Move $169$ to the left of $π$ .

$\frac{169 \cdot π}{18} + 2 (π) (\frac{13}{6}) (\frac{3}{2})$

Step 3.7

Cancel the common factor of $2$ .

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Step 3.7.1

Factor $2$ out of $2 (π) (\frac{13}{6})$ .

$\frac{169 π}{18} + 2 ((π) (\frac{13}{6})) \frac{3}{2}$

Step 3.7.2

Cancel the common factor.

$\frac{169 π}{18} + 2 ((π) (\frac{13}{6})) \frac{3}{2}$

Step 3.7.3

Rewrite the expression.

$\frac{169 π}{18} + (π) (\frac{13}{6}) \cdot 3$

Step 3.8

Combine $π$ and $\frac{13}{6}$ .

$\frac{169 π}{18} + \frac{π \cdot 13}{6} \cdot 3$

Step 3.9

Combine $\frac{π \cdot 13}{6}$ and $3$ .

$\frac{169 π}{18} + \frac{π \cdot 13 \cdot 3}{6}$

Step 3.10

Multiply $3$ by $13$ .

$\frac{169 π}{18} + \frac{π \cdot 39}{6}$

Step 3.11

Cancel the common factor of $39$ and $6$ .

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Step 3.11.1

Factor $3$ out of $π \cdot 39$ .

$\frac{169 π}{18} + \frac{3 (π \cdot 13)}{6}$

Step 3.11.2

Cancel the common factors.

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Step 3.11.2.1

Factor $3$ out of $6$ .

$\frac{169 π}{18} + \frac{3 (π \cdot 13)}{3 (2)}$

Step 3.11.2.2

Cancel the common factor.

$\frac{169 π}{18} + \frac{3 (π \cdot 13)}{3 \cdot 2}$

Step 3.11.2.3

Rewrite the expression.

$\frac{169 π}{18} + \frac{π \cdot 13}{2}$

Step 3.12

Move $13$ to the left of $π$ .

$\frac{169 π}{18} + \frac{13 π}{2}$

Step 4

To write $\frac{13 π}{2}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{169 π}{18} + \frac{13 π}{2} \cdot \frac{9}{9}$

Step 5

Write each expression with a common denominator of $18$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.1

Multiply $\frac{13 π}{2}$ by $\frac{9}{9}$ .

$\frac{169 π}{18} + \frac{13 π \cdot 9}{2 \cdot 9}$

Step 5.2

Multiply $2$ by $9$ .

$\frac{169 π}{18} + \frac{13 π \cdot 9}{18}$

Step 6

Combine the numerators over the common denominator.

$\frac{169 π + 13 π \cdot 9}{18}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply $9$ by $13$ .

$\frac{169 π + 117 π}{18}$

Step 7.2

Add $169 π$ and $117 π$ .

$\frac{286 π}{18}$

Step 8

Cancel the common factor of $286$ and $18$ .

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Step 8.1

Factor $2$ out of $286 π$ .

$\frac{2 (143 π)}{18}$

Step 8.2

Cancel the common factors.

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Step 8.2.1

Factor $2$ out of $18$ .

$\frac{2 (143 π)}{2 (9)}$

Step 8.2.2

Cancel the common factor.

$\frac{2 (143 π)}{2 \cdot 9}$

Step 8.2.3

Rewrite the expression.

$\frac{143 π}{9}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{143 π}{9}$

Decimal Form:

$49.91641660 \dots$