Pre-Algebra Examples

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

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 $r = 4$ and height $h = 4$ into the formula to find the volume of the cone. Pi $π$ is approximately equal to $3.14$ .

$\frac{1}{3} \cdot π \cdot 4^{2} \cdot 4$

Step 3

Multiply $4^{2}$ by $4$ by adding the exponents.

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Step 3.1

Move $4$ .

$\frac{1}{3} \cdot π \cdot (4 \cdot 4^{2})$

Step 3.2

Multiply $4$ by $4^{2}$ .

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Step 3.2.1

Raise $4$ to the power of $1$ .

$\frac{1}{3} \cdot π \cdot (4^{1} \cdot 4^{2})$

Step 3.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{1}{3} \cdot π \cdot 4^{1 + 2}$

Step 3.3

Add $1$ and $2$ .

$\frac{1}{3} \cdot π \cdot 4^{3}$

Step 4

Combine $\frac{1}{3}$ and $π$ .

$\frac{π}{3} \cdot 4^{3}$

Step 5

Raise $4$ to the power of $3$ .

$\frac{π}{3} \cdot 64$

Step 6

Combine $\frac{π}{3}$ and $64$ .

$\frac{π \cdot 64}{3}$

Step 7

Move $64$ to the left of $π$ .

$\frac{64 π}{3} {(yd)}^{3}$