Pre-Algebra Examples

 $\begin{array}{r} h = & 3 \\ r = & 6 \end{array}$

The surface area of a cone is equal to the area of the base plus the area of the cone.

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

Substitute the values of the length $(r = 6)$ , the height $(h = 3)$ , and an approximation for $π (3.14)$ into the formula.

$(3.14) {(6)}^{2} + 3.14 (6) \sqrt{{(6)}^{2} + {(3)}^{2}}$

Simplify each term.

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

$3.14 \cdot 36 + 3.14 (6) \sqrt{{(6)}^{2} + {(3)}^{2}}$

Multiply $3.14$ by $36$ .

$113.04 + 3.14 (6) \sqrt{{(6)}^{2} + {(3)}^{2}}$

Multiply $3.14$ by $6$ .

$113.04 + 18.84 \sqrt{{(6)}^{2} + {(3)}^{2}}$

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

$113.04 + 18.84 \sqrt{36 + {(3)}^{2}}$

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

$113.04 + 18.84 \sqrt{36 + 9}$

Add $36$ and $9$ .

$113.04 + 18.84 \sqrt{45}$

Rewrite $45$ as $3^{2} \cdot 5$ .

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Factor $9$ out of $45$ .

$113.04 + 18.84 \sqrt{9 (5)}$

Rewrite $9$ as $3^{2}$ .

$113.04 + 18.84 \sqrt{3^{2} \cdot 5}$

Pull terms out from under the radical.

$113.04 + 18.84 (3 \sqrt{5})$

Multiply $18.84 (3 \sqrt{5})$ .

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Multiply $3$ by $18.84$ .

$113.04 + 56.52 \sqrt{5}$

Multiply $56.52$ by $\sqrt{5}$ .

$113.04 + 126.38256208$

Add $113.04$ and $126.38256208$ .

$239.42256208$

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