Pre-Algebra Examples

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$\begin{array}{r} h = & 5 \\ r = & 5 \end{array}$

Step 1

The volume of a cone is equal to

$\frac{1}{3}$ times the area of the base

$π r^{2}$ times the height

$h$ .

$\frac{1}{3} \cdot π \cdot {(r a d i u s)}^{2} \cdot (h e i g h t)$

Step 2

Substitute the values of the radius

$r = 5$ and height

$h = 5$ into the formula to find the volume of the cone. Pi

$π$ is approximately equal to

$3.14$ .

$\frac{1}{3} \cdot π \cdot 5^{2} \cdot 5$

Step 3

Multiply

$5^{2}$ by

$5$ by adding the exponents.

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Step 3.1

Move

$5$ .

$\frac{1}{3} \cdot π \cdot (5 \cdot 5^{2})$

Step 3.2

Multiply

$5$ by

$5^{2}$ .

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Step 3.2.1

Raise

$5$ to the power of

$1$ .

$\frac{1}{3} \cdot π \cdot (5^{1} \cdot 5^{2})$

Step 3.2.2

Use the power rule

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{1}{3} \cdot π \cdot 5^{1 + 2}$

Step 3.3

Add

$1$ and

$2$ .

$\frac{1}{3} \cdot π \cdot 5^{3}$

Step 4

Combine

$\frac{1}{3}$ and

$π$ .

$\frac{π}{3} \cdot 5^{3}$

Step 5

Raise

$5$ to the power of

$3$ .

$\frac{π}{3} \cdot 125$

Step 6

Combine

$\frac{π}{3}$ and

$125$ .

$\frac{π \cdot 125}{3}$

Step 7

Move

$125$ to the left of

$π$ .

$\frac{125 π}{3}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{125 π}{3}$

Decimal Form:

$130.89969389 \dots$

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