Basic Math Examples

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\begin{matrix} h = & 2 r = & 4 \end{matrix}

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

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}})

$(π \cdot (r a d i u s)) \cdot ((r a d i u s) + \sqrt{{(r a d i u s)}^{2} + {(h e i g h t)}^{2}})$

Step 2

Substitute the values of the length

r = 4

$r = 4$ and height

h = 2

$h = 2$ into the formula. Pi

π

$π$ is approximately equal to

3.14

$3.14$ .

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

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

Step 3

Move

4

$4$ to the left of

π

$π$ .

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

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

Step 4

Simplify each term.

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Step 4.1

Raise

4

$4$ to the power of

2

$2$ .

4 π (4 + \sqrt{16 + {(2)}^{2}})

$4 π (4 + \sqrt{16 + {(2)}^{2}})$

Step 4.2

Raise

2

$2$ to the power of

2

$2$ .

4 π (4 + \sqrt{16 + 4})

$4 π (4 + \sqrt{16 + 4})$

Step 4.3

Add

16

$16$ and

4

$4$ .

4 π (4 + \sqrt{20})

$4 π (4 + \sqrt{20})$

Step 4.4

Rewrite

20

$20$ as

2^{2} \cdot 5

$2^{2} \cdot 5$ .

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Step 4.4.1

Factor

4

$4$ out of

20

$20$ .

4 π (4 + \sqrt{4 (5)})

$4 π (4 + \sqrt{4 (5)})$

Step 4.4.2

Rewrite

4

$4$ as

2^{2}

$2^{2}$ .

4 π (4 + \sqrt{2^{2} \cdot 5})

$4 π (4 + \sqrt{2^{2} \cdot 5})$

4 π (4 + \sqrt{2^{2} \cdot 5})

$4 π (4 + \sqrt{2^{2} \cdot 5})$

Step 4.5

Pull terms out from under the radical.

4 π (4 + 2 \sqrt{5})

$4 π (4 + 2 \sqrt{5})$

4 π (4 + 2 \sqrt{5})

$4 π (4 + 2 \sqrt{5})$

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})

$4 π \cdot 4 + 4 π (2 \sqrt{5})$

Step 5.2

Multiply.

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Step 5.2.1

Multiply

4

$4$ by

4

$4$ .

16 π + 4 π (2 \sqrt{5})

$16 π + 4 π (2 \sqrt{5})$

Step 5.2.2

Multiply

2

$2$ by

4

$4$ .

16 π + 8 π \sqrt{5}

$16 π + 8 π \sqrt{5}$

16 π + 8 π \sqrt{5}

$16 π + 8 π \sqrt{5}$

16 π + 8 π \sqrt{5}

$16 π + 8 π \sqrt{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

16 π + 8 π \sqrt{5}

$16 π + 8 π \sqrt{5}$

Decimal Form:

106.46400030 \dots

$106.46400030 \dots$

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