Pre-Algebra Examples

 $\begin{array}{r} h = & 8 \\ r = & 12 \end{array}$

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 $r = 12$ and height $h = 8$ into the formula to find the volume of the cone. Pi $π$ is approximately equal to $3.14$ .

$\frac{1}{3} \cdot π \cdot 12^{2} \cdot 8$

Step 3

Combine $\frac{1}{3}$ and $π$ .

$\frac{π}{3} \cdot 12^{2} \cdot 8$

Step 4

Raise $12$ to the power of $2$ .

$\frac{π}{3} \cdot 144 \cdot 8$

Step 5

Cancel the common factor of $3$ .

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Step 5.1

Factor $3$ out of $144$ .

$\frac{π}{3} \cdot (3 (48)) \cdot 8$

Step 5.2

Cancel the common factor.

$\frac{π}{3} \cdot (3 \cdot 48) \cdot 8$

Step 5.3

Rewrite the expression.

$π \cdot 48 \cdot 8$

Step 6

Simplify the expression.

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Step 6.1

Move $48$ to the left of $π$ .

$48 \cdot π \cdot 8$

Step 6.2

Multiply $8$ by $48$ .

$384 π$

Step 7

The result can be shown in multiple forms.

Exact Form:

$384 π$

Decimal Form:

$1206.37157897 \dots$