Pre-Algebra Examples

 $\begin{array}{r} h = & 2 \\ r = & 4 \end{array}$

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 $r = 4$ and height $h = 2$ into the formula. Pi $π$ is approximately equal to $3.14$ .

$(π \cdot 4) (4 + \sqrt{{(4)}^{2} + {(2)}^{2}})$

Step 3

Move $4$ to the left of $π$ .

$4 \cdot π (4 + \sqrt{{(4)}^{2} + {(2)}^{2}})$

Step 4

Simplify each term.

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Step 4.1

Raise $4$ to the power of $2$ .

$4 π (4 + \sqrt{16 + {(2)}^{2}})$

Step 4.2

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

$4 π (4 + \sqrt{16 + 4})$

Step 4.3

Add $16$ and $4$ .

$4 π (4 + \sqrt{20})$

Step 4.4

Rewrite $20$ as $2^{2} \cdot 5$ .

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Step 4.4.1

Factor $4$ out of $20$ .

$4 π (4 + \sqrt{4 (5)})$

Step 4.4.2

Rewrite $4$ as $2^{2}$ .

$4 π (4 + \sqrt{2^{2} \cdot 5})$

Step 4.5

Pull terms out from under the radical.

$4 π (4 + 2 \sqrt{5})$

Step 5

Simplify by multiplying through.

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Step 5.1

Apply the distributive property.

$4 π \cdot 4 + 4 π (2 \sqrt{5})$

Step 5.2

Multiply.

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Step 5.2.1

Multiply $4$ by $4$ .

$16 π + 4 π (2 \sqrt{5})$

Step 5.2.2

Multiply $2$ by $4$ .

$16 π + 8 π \sqrt{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$16 π + 8 π \sqrt{5}$

Decimal Form:

$106.46400030 \dots$

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