Pre-Algebra Examples

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$\begin{array}{r} h = & 1 \\ r = & 4 \end{array}$

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

$h = 1$ into the formula. Pi

$π$ is approximately equal to

$3.14$ .

$(π \cdot 4) (4 + \sqrt{{(4)}^{2} + {(1)}^{2}})$

Step 3

Move

$4$ to the left of

$π$ .

$4 \cdot π (4 + \sqrt{{(4)}^{2} + {(1)}^{2}})$

Step 4

Simplify each term.

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Step 4.1

Raise

$4$ to the power of

$2$ .

$4 π (4 + \sqrt{16 + {(1)}^{2}})$

Step 4.2

One to any power is one.

$4 π (4 + \sqrt{16 + 1})$

Step 4.3

Add

$16$ and

$1$ .

$4 π (4 + \sqrt{17})$

Step 5

Simplify by multiplying through.

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Step 5.1

Apply the distributive property.

$4 π \cdot 4 + 4 π \sqrt{17}$

Step 5.2

Multiply

$4$ by

$4$ .

$16 π + 4 π \sqrt{17}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$16 π + 4 π \sqrt{17}$

Decimal Form:

$102.07795583 \dots$

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