Pre-Algebra Examples

 $\begin{array}{r} h = & 12 \\ r = & 9 \end{array}$

Step 1

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

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

Step 2

Substitute the values of the length $r = 9$ and height $h = 12$ into the formula. Pi $π$ is approximately equal to $3.14$ .

$(π \cdot 9) (9 + \sqrt{{(9)}^{2} + {(12)}^{2}})$

Step 3

Move $9$ to the left of $π$ .

$9 \cdot π (9 + \sqrt{{(9)}^{2} + {(12)}^{2}})$

Step 4

Simplify each term.

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Step 4.1

Raise $9$ to the power of $2$ .

$9 π (9 + \sqrt{81 + {(12)}^{2}})$

Step 4.2

Raise $12$ to the power of $2$ .

$9 π (9 + \sqrt{81 + 144})$

Step 4.3

Add $81$ and $144$ .

$9 π (9 + \sqrt{225})$

Step 4.4

Rewrite $225$ as $15^{2}$ .

$9 π (9 + \sqrt{15^{2}})$

Step 4.5

Pull terms out from under the radical, assuming positive real numbers.

$9 π (9 + 15)$

Step 5

Simplify the expression.

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Step 5.1

Add $9$ and $15$ .

$9 π \cdot 24$

Step 5.2

Multiply $24$ by $9$ .

$216 π$

Step 6

The result can be shown in multiple forms.

Exact Form:

$216 π$

Decimal Form:

$678.58401317 \dots$