Find the Surface Area cone (9)(6)

 $\begin{array}{r} h = & 9 \\ r = & 6 \end{array}$

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 $r = 6$ and height $h = 9$ into the formula. Pi $π$ is approximately equal to $3.14$ .

$(π \cdot 6) (6 + \sqrt{{(6)}^{2} + {(9)}^{2}})$

Step 3

Move $6$ to the left of $π$ .

$6 \cdot π (6 + \sqrt{{(6)}^{2} + {(9)}^{2}})$

Step 4

Simplify each term.

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

$6 π (6 + \sqrt{36 + {(9)}^{2}})$

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

$6 π (6 + \sqrt{36 + 81})$

Add $36$ and $81$ .

$6 π (6 + \sqrt{117})$

Rewrite $117$ as $3^{2} \cdot 13$ .

Factor $9$ out of $117$ .

$6 π (6 + \sqrt{9 (13)})$

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

$6 π (6 + \sqrt{3^{2} \cdot 13})$

Pull terms out from under the radical.

$6 π (6 + 3 \sqrt{13})$

Step 5

Simplify by multiplying through.

Apply the distributive property.

$6 π \cdot 6 + 6 π (3 \sqrt{13})$

Multiply.

Multiply $6$ by $6$ .

$36 π + 6 π (3 \sqrt{13})$

Multiply $3$ by $6$ .

$36 π + 18 π \sqrt{13}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$36 π + 18 π \sqrt{13}$

Decimal Form:

$316.98645671 \dots$