Pre-Algebra Examples

 $\begin{array}{r} h = & 5 \\ r = & 3 \end{array}$

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 $r = 3$ and height $h = 5$ into the formula. Pi $π$ is approximately equal to $3.14$ .

$(π \cdot 3) (3 + \sqrt{{(3)}^{2} + {(5)}^{2}})$

Step 3

Move $3$ to the left of $π$ .

$3 \cdot π (3 + \sqrt{{(3)}^{2} + {(5)}^{2}})$

Step 4

Simplify each term.

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Step 4.1

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

$3 π (3 + \sqrt{9 + {(5)}^{2}})$

Step 4.2

Raise $5$ to the power of $2$ .

$3 π (3 + \sqrt{9 + 25})$

Step 4.3

Add $9$ and $25$ .

$3 π (3 + \sqrt{34})$

Step 5

Simplify by multiplying through.

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Step 5.1

Apply the distributive property.

$3 π \cdot 3 + 3 π \sqrt{34}$

Step 5.2

Multiply $3$ by $3$ .

$9 π + 3 π \sqrt{34}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$9 π + 3 π \sqrt{34}$

Decimal Form:

$83.22976079 \dots$

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