Find the Surface Area cone (10)(5)

 $\begin{array}{r} h = & 10 \\ r = & 5 \end{array}$

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 $r = 5$ and height $h = 10$ into the formula. Pi $π$ is approximately equal to $3.14$ .

$(π \cdot 5) (5 + \sqrt{{(5)}^{2} + {(10)}^{2}})$

Step 3

Move $5$ to the left of $π$ .

$5 \cdot π (5 + \sqrt{{(5)}^{2} + {(10)}^{2}})$

Step 4

Simplify each term.

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

$5 π (5 + \sqrt{25 + {(10)}^{2}})$

Raise $10$ to the power of $2$ .

$5 π (5 + \sqrt{25 + 100})$

Add $25$ and $100$ .

$5 π (5 + \sqrt{125})$

Rewrite $125$ as $5^{2} \cdot 5$ .

Factor $25$ out of $125$ .

$5 π (5 + \sqrt{25 (5)})$

Rewrite $25$ as $5^{2}$ .

$5 π (5 + \sqrt{5^{2} \cdot 5})$

Pull terms out from under the radical.

$5 π (5 + 5 \sqrt{5})$

Step 5

Simplify by multiplying through.

Apply the distributive property.

$5 π \cdot 5 + 5 π (5 \sqrt{5})$

Multiply.

Multiply $5$ by $5$ .

$25 π + 5 π (5 \sqrt{5})$

Multiply $5$ by $5$ .

$25 π + 25 π \sqrt{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$25 π + 25 π \sqrt{5}$

Decimal Form:

$254.16018461 \dots$