Basic Math Examples

 $\begin{array}{r} h = & 7 \\ r = & 1 \end{array}$

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 $r = 1$ and height $h = 7$ into the formula. Pi $π$ is approximately equal to $3.14$ .

$(π \cdot 1) (1 + \sqrt{{(1)}^{2} + {(7)}^{2}})$

Step 3

Multiply $π$ by $1$ .

$π (1 + \sqrt{{(1)}^{2} + {(7)}^{2}})$

Step 4

Simplify each term.

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Step 4.1

One to any power is one.

$π (1 + \sqrt{1 + {(7)}^{2}})$

Step 4.2

Raise $7$ to the power of $2$ .

$π (1 + \sqrt{1 + 49})$

Step 4.3

Add $1$ and $49$ .

$π (1 + \sqrt{50})$

Step 4.4

Rewrite $50$ as $5^{2} \cdot 2$ .

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Step 4.4.1

Factor $25$ out of $50$ .

$π (1 + \sqrt{25 (2)})$

Step 4.4.2

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

$π (1 + \sqrt{5^{2} \cdot 2})$

Step 4.5

Pull terms out from under the radical.

$π (1 + 5 \sqrt{2})$

Step 5

Simplify by multiplying through.

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Step 5.1

Apply the distributive property.

$π \cdot 1 + π (5 \sqrt{2})$

Step 5.2

Multiply $π$ by $1$ .

$π + π (5 \sqrt{2})$

Step 6

Move $5$ to the left of $π$ .

$π + 5 π \sqrt{2}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$π + 5 π \sqrt{2}$

Decimal Form:

$25.35600734 \dots$