Basic Math Examples



$\begin{array}{r} h = & 12 \\ r = & 5 \end{array}$

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

$h = 12$ into the formula. Pi

$π$ is approximately equal to

$3.14$ .

$(π \cdot 5) (5 + \sqrt{{(5)}^{2} + {(12)}^{2}})$

Step 3

Move

$5$ to the left of

$π$ .

$5 \cdot π (5 + \sqrt{{(5)}^{2} + {(12)}^{2}})$

Step 4

Simplify each term.

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Step 4.1

Raise

$5$ to the power of

$2$ .

$5 π (5 + \sqrt{25 + {(12)}^{2}})$

Step 4.2

Raise

$12$ to the power of

$2$ .

$5 π (5 + \sqrt{25 + 144})$

Step 4.3

Add

$25$ and

$144$ .

$5 π (5 + \sqrt{169})$

Step 4.4

Rewrite

$169$ as

$13^{2}$ .

$5 π (5 + \sqrt{13^{2}})$

Step 4.5

Pull terms out from under the radical, assuming positive real numbers.

$5 π (5 + 13)$

Step 5

Simplify the expression.

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Step 5.1

Add

$5$ and

$13$ .

$5 π \cdot 18$

Step 5.2

Multiply

$18$ by

$5$ .

$90 π$

Step 6

The result can be shown in multiple forms.

Exact Form:

$90 π$

Decimal Form:

$282.74333882 \dots$