Basic Math Examples



\begin{array}{r} h = & 15 \\ r = & 6 \end{array}

$\begin{array}{r} h = & 15 \\ r = & 6 \end{array}$

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}})

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

Step 2

Substitute the values of the length

r = 6

$r = 6$ and height

h = 15

$h = 15$ into the formula. Pi

π

$π$ is approximately equal to

3.14

$3.14$ .

(π \cdot 6) (6 + \sqrt{{(6)}^{2} + {(15)}^{2}})

$(π \cdot 6) (6 + \sqrt{{(6)}^{2} + {(15)}^{2}})$

Step 3

Move

6

$6$ to the left of

π

$π$ .

6 \cdot π (6 + \sqrt{{(6)}^{2} + {(15)}^{2}})

$6 \cdot π (6 + \sqrt{{(6)}^{2} + {(15)}^{2}})$

Step 4

Simplify each term.

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Step 4.1

Raise

6

$6$ to the power of

2

$2$ .

6 π (6 + \sqrt{36 + {(15)}^{2}})

$6 π (6 + \sqrt{36 + {(15)}^{2}})$

Step 4.2

Raise

15

$15$ to the power of

2

$2$ .

6 π (6 + \sqrt{36 + 225})

$6 π (6 + \sqrt{36 + 225})$

Step 4.3

Add

36

$36$ and

225

$225$ .

6 π (6 + \sqrt{261})

$6 π (6 + \sqrt{261})$

Step 4.4

Rewrite

261

$261$ as

3^{2} \cdot 29

$3^{2} \cdot 29$ .

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Step 4.4.1

Factor

9

$9$ out of

261

$261$ .

6 π (6 + \sqrt{9 (29)})

$6 π (6 + \sqrt{9 (29)})$

Step 4.4.2

Rewrite

9

$9$ as

3^{2}

$3^{2}$ .

6 π (6 + \sqrt{3^{2} \cdot 29})

$6 π (6 + \sqrt{3^{2} \cdot 29})$

6 π (6 + \sqrt{3^{2} \cdot 29})

$6 π (6 + \sqrt{3^{2} \cdot 29})$

Step 4.5

Pull terms out from under the radical.

6 π (6 + 3 \sqrt{29})

$6 π (6 + 3 \sqrt{29})$

6 π (6 + 3 \sqrt{29})

$6 π (6 + 3 \sqrt{29})$

Step 5

Simplify by multiplying through.

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Step 5.1

Apply the distributive property.

6 π \cdot 6 + 6 π (3 \sqrt{29})

$6 π \cdot 6 + 6 π (3 \sqrt{29})$

Step 5.2

Multiply.

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Step 5.2.1

Multiply

6

$6$ by

6

$6$ .

36 π + 6 π (3 \sqrt{29})

$36 π + 6 π (3 \sqrt{29})$

Step 5.2.2

Multiply

3

$3$ by

6

$6$ .

36 π + 18 π \sqrt{29}

$36 π + 18 π \sqrt{29}$

36 π + 18 π \sqrt{29}

$36 π + 18 π \sqrt{29}$

36 π + 18 π \sqrt{29}

$36 π + 18 π \sqrt{29}$

Step 6

The result can be shown in multiple forms.

Exact Form:

36 π + 18 π \sqrt{29}

$36 π + 18 π \sqrt{29}$

Decimal Form:

417.62123106 \dots

$417.62123106 \dots$