Pre-Algebra Examples

 $\begin{array}{r} h = & 24 \\ r = & \frac{1}{2} \end{array}$

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 $r = \frac{1}{2}$ and height $h = 24$ into the formula. Pi $π$ is approximately equal to $3.14$ .

$2 (π) {(\frac{1}{2})}^{2} + 2 (π) (\frac{1}{2}) (24)$

Step 3

Simplify each term.

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Step 3.1

Apply the product rule to $\frac{1}{2}$ .

$2 π \frac{1^{2}}{2^{2}} + 2 (π) (\frac{1}{2}) (24)$

Step 3.2

One to any power is one.

$2 π \frac{1}{2^{2}} + 2 (π) (\frac{1}{2}) (24)$

Step 3.3

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

$2 π \frac{1}{4} + 2 (π) (\frac{1}{2}) (24)$

Step 3.4

Cancel the common factor of $2$ .

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Step 3.4.1

Factor $2$ out of $2 π$ .

$2 (π) \frac{1}{4} + 2 (π) (\frac{1}{2}) (24)$

Step 3.4.2

Factor $2$ out of $4$ .

$2 (π) \frac{1}{2 (2)} + 2 (π) (\frac{1}{2}) (24)$

Step 3.4.3

Cancel the common factor.

$2 π \frac{1}{2 \cdot 2} + 2 (π) (\frac{1}{2}) (24)$

Step 3.4.4

Rewrite the expression.

$π \frac{1}{2} + 2 (π) (\frac{1}{2}) (24)$

Step 3.5

Combine $π$ and $\frac{1}{2}$ .

$\frac{π}{2} + 2 (π) (\frac{1}{2}) (24)$

Step 3.6

Cancel the common factor of $2$ .

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Step 3.6.1

Cancel the common factor.

$\frac{π}{2} + 2 π \frac{1}{2} \cdot 24$

Step 3.6.2

Rewrite the expression.

$\frac{π}{2} + π \cdot 24$

Step 3.7

Move $24$ to the left of $π$ .

$\frac{π}{2} + 24 π$

Step 4

To write $24 π$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{π}{2} + 24 π \cdot \frac{2}{2}$

Step 5

Combine fractions.

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Step 5.1

Combine $24 π$ and $\frac{2}{2}$ .

$\frac{π}{2} + \frac{24 π \cdot 2}{2}$

Step 5.2

Combine the numerators over the common denominator.

$\frac{π + 24 π \cdot 2}{2}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $2$ by $24$ .

$\frac{π + 48 π}{2}$

Step 6.2

Add $π$ and $48 π$ .

$\frac{49 π}{2}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{49 π}{2}$

Decimal Form:

$76.96902001 \dots$