Basic Math Examples

 $\begin{array}{r} h = & 18 \\ r = & 6 \end{array}$

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 $h = 18$ into the formula. Pi $π$ is approximately equal to $3.14$ .

$(π \cdot 6) (6 + \sqrt{{(6)}^{2} + {(18)}^{2}})$

Step 3

Move $6$ to the left of $π$ .

$6 \cdot π (6 + \sqrt{{(6)}^{2} + {(18)}^{2}})$

Step 4

Simplify each term.

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Step 4.1

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

$6 π (6 + \sqrt{36 + {(18)}^{2}})$

Step 4.2

Raise $18$ to the power of $2$ .

$6 π (6 + \sqrt{36 + 324})$

Step 4.3

Add $36$ and $324$ .

$6 π (6 + \sqrt{360})$

Step 4.4

Rewrite $360$ as $6^{2} \cdot 10$ .

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Step 4.4.1

Factor $36$ out of $360$ .

$6 π (6 + \sqrt{36 (10)})$

Step 4.4.2

Rewrite $36$ as $6^{2}$ .

$6 π (6 + \sqrt{6^{2} \cdot 10})$

Step 4.5

Pull terms out from under the radical.

$6 π (6 + 6 \sqrt{10})$

Step 5

Simplify by multiplying through.

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Step 5.1

Apply the distributive property.

$6 π \cdot 6 + 6 π (6 \sqrt{10})$

Step 5.2

Multiply.

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Step 5.2.1

Multiply $6$ by $6$ .

$36 π + 6 π (6 \sqrt{10})$

Step 5.2.2

Multiply $6$ by $6$ .

$36 π + 36 π \sqrt{10}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$36 π + 36 π \sqrt{10}$

Decimal Form:

$470.74251309 \dots$