Pre-Algebra Examples

 $\begin{array}{r} h = & 7 yd \\ r = & 2 yd \end{array}$

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 $r = 2$ and height $h = 7$ into the formula. Pi $π$ is approximately equal to $3.14$ .

$2 (π) {(2)}^{2} + 2 (π) (2) (7)$

Step 3

Simplify each term.

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Step 3.1

Multiply $2$ by ${(2)}^{2}$ by adding the exponents.

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Step 3.1.1

Move ${(2)}^{2}$ .

${(2)}^{2} \cdot 2 π + 2 (π) (2) (7)$

Step 3.1.2

Multiply ${(2)}^{2}$ by $2$ .

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Step 3.1.2.1

Raise $2$ to the power of $1$ .

${(2)}^{2} \cdot 2^{1} π + 2 (π) (2) (7)$

Step 3.1.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2^{2 + 1} π + 2 (π) (2) (7)$

Step 3.1.3

Add $2$ and $1$ .

$2^{3} π + 2 (π) (2) (7)$

Step 3.2

Raise $2$ to the power of $3$ .

$8 π + 2 (π) (2) (7)$

Step 3.3

Multiply $2$ by $2$ .

$8 π + 4 π \cdot 7$

Step 3.4

Multiply $7$ by $4$ .

$8 π + 28 π$

Step 4

Add $8 π$ and $28 π$ .

$36 π {(yd)}^{2}$