Find the Surface Area cone (6)(4)

 $\begin{array}{r} h = & 6 \\ r = & 4 \end{array}$

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

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

Substitute the values of the length $r = 4$ and height $h = 6$ into the formula. Pi $π$ is approximately equal to $3.14$ .

$(π \cdot 4) (4 + \sqrt{{(4)}^{2} + {(6)}^{2}})$

Move $4$ to the left of $π$ .

$4 \cdot π (4 + \sqrt{{(4)}^{2} + {(6)}^{2}})$

Simplify each term.

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Raise $4$ to the power of $2$ .

$4 π (4 + \sqrt{16 + {(6)}^{2}})$

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

$4 π (4 + \sqrt{16 + 36})$

Add $16$ and $36$ .

$4 π (4 + \sqrt{52})$

Rewrite $52$ as $2^{2} \cdot 13$ .

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Factor $4$ out of $52$ .

$4 π (4 + \sqrt{4 (13)})$

Rewrite $4$ as $2^{2}$ .

$4 π (4 + \sqrt{2^{2} \cdot 13})$

Pull terms out from under the radical.

$4 π (4 + 2 \sqrt{13})$

Simplify by multiplying through.

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Apply the distributive property.

$4 π \cdot 4 + 4 π (2 \sqrt{13})$

Multiply.

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Multiply $4$ by $4$ .

$16 π + 4 π (2 \sqrt{13})$

Multiply $2$ by $4$ .

$16 π + 8 π \sqrt{13}$

The result can be shown in multiple forms.

Exact Form:

$16 π + 8 π \sqrt{13}$

Decimal Form:

$140.88286965 \dots$

Find the Surface Area cone (6)(4)

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