Find the Surface Area cone (15)(6)



$\begin{array}{r} h = & 15 \\ r = & 6 \end{array}$

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

$h = 15$ into the formula. Pi

$π$ is approximately equal to

$3.14$ .

$(π \cdot 6) (6 + \sqrt{{(6)}^{2} + {(15)}^{2}})$

Step 3

Move

$6$ to the left of

$π$ .

$6 \cdot π (6 + \sqrt{{(6)}^{2} + {(15)}^{2}})$

Step 4

Simplify each term.

Raise

$6$ to the power of

$2$ .

$6 π (6 + \sqrt{36 + {(15)}^{2}})$

Raise

$15$ to the power of

$2$ .

$6 π (6 + \sqrt{36 + 225})$

Add

$36$ and

$225$ .

$6 π (6 + \sqrt{261})$

Rewrite

$261$ as

$3^{2} \cdot 29$ .

Factor

$9$ out of

$261$ .

$6 π (6 + \sqrt{9 (29)})$

Rewrite

$9$ as

$3^{2}$ .

$6 π (6 + \sqrt{3^{2} \cdot 29})$

Pull terms out from under the radical.

$6 π (6 + 3 \sqrt{29})$

Step 5

Simplify by multiplying through.

Apply the distributive property.

$6 π \cdot 6 + 6 π (3 \sqrt{29})$

Multiply.

Multiply

$6$ by

$6$ .

$36 π + 6 π (3 \sqrt{29})$

Multiply

$3$ by

$6$ .

$36 π + 18 π \sqrt{29}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$36 π + 18 π \sqrt{29}$

Decimal Form:

$417.62123106 \dots$

Find the Surface Area cone (15)(6)

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