Find the Surface Area cone (15)(10)



$\begin{array}{r} h = & 15 \\ r = & 10 \end{array}$

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

$r = 10$ and height

$h = 15$ into the formula. Pi

$π$ is approximately equal to

$3.14$ .

$(π \cdot 10) (10 + \sqrt{{(10)}^{2} + {(15)}^{2}})$

Step 3

Move

$10$ to the left of

$π$ .

$10 \cdot π (10 + \sqrt{{(10)}^{2} + {(15)}^{2}})$

Step 4

Simplify each term.

Raise

$10$ to the power of

$2$ .

$10 π (10 + \sqrt{100 + {(15)}^{2}})$

Raise

$15$ to the power of

$2$ .

$10 π (10 + \sqrt{100 + 225})$

Add

$100$ and

$225$ .

$10 π (10 + \sqrt{325})$

Rewrite

$325$ as

$5^{2} \cdot 13$ .

Factor

$25$ out of

$325$ .

$10 π (10 + \sqrt{25 (13)})$

Rewrite

$25$ as

$5^{2}$ .

$10 π (10 + \sqrt{5^{2} \cdot 13})$

Pull terms out from under the radical.

$10 π (10 + 5 \sqrt{13})$

Step 5

Simplify by multiplying through.

Apply the distributive property.

$10 π \cdot 10 + 10 π (5 \sqrt{13})$

Multiply.

Multiply

$10$ by

$10$ .

$100 π + 10 π (5 \sqrt{13})$

Multiply

$5$ by

$10$ .

$100 π + 50 π \sqrt{13}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$100 π + 50 π \sqrt{13}$

Decimal Form:

$880.51793531 \dots$

Find the Surface Area cone (15)(10)

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