Pre-Algebra Examples

 $\begin{array}{r} h = & 20 \\ r = & 50 \end{array}$

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 $r = 50$ and height $h = 20$ into the formula. Pi $π$ is approximately equal to $3.14$ .

$(π \cdot 50) (50 + \sqrt{{(50)}^{2} + {(20)}^{2}})$

Step 3

Move $50$ to the left of $π$ .

$50 \cdot π (50 + \sqrt{{(50)}^{2} + {(20)}^{2}})$

Step 4

Simplify each term.

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Step 4.1

Raise $50$ to the power of $2$ .

$50 π (50 + \sqrt{2500 + {(20)}^{2}})$

Step 4.2

Raise $20$ to the power of $2$ .

$50 π (50 + \sqrt{2500 + 400})$

Step 4.3

Add $2500$ and $400$ .

$50 π (50 + \sqrt{2900})$

Step 4.4

Rewrite $2900$ as $10^{2} \cdot 29$ .

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Step 4.4.1

Factor $100$ out of $2900$ .

$50 π (50 + \sqrt{100 (29)})$

Step 4.4.2

Rewrite $100$ as $10^{2}$ .

$50 π (50 + \sqrt{10^{2} \cdot 29})$

Step 4.5

Pull terms out from under the radical.

$50 π (50 + 10 \sqrt{29})$

Step 5

Simplify by multiplying through.

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Step 5.1

Apply the distributive property.

$50 π \cdot 50 + 50 π (10 \sqrt{29})$

Step 5.2

Multiply.

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Step 5.2.1

Multiply $50$ by $50$ .

$2500 π + 50 π (10 \sqrt{29})$

Step 5.2.2

Multiply $10$ by $50$ .

$2500 π + 500 π \sqrt{29}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$2500 π + 500 π \sqrt{29}$

Decimal Form:

$16312.97873220 \dots$