Find the Volume cone (12)(5)

 $\begin{array}{r} h = & 12 \\ r = & 5 \end{array}$

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

$\frac{1}{3} \cdot π \cdot 5^{2} \cdot 12$

Step 3

Combine $\frac{1}{3}$ and $π$ .

$\frac{π}{3} \cdot 5^{2} \cdot 12$

Step 4

Raise $5$ to the power of $2$ .

$\frac{π}{3} \cdot 25 \cdot 12$

Step 5

Combine $\frac{π}{3}$ and $25$ .

$\frac{π \cdot 25}{3} \cdot 12$

Step 6

Cancel the common factor of $3$ .

Factor $3$ out of $12$ .

$\frac{π \cdot 25}{3} \cdot (3 (4))$

Cancel the common factor.

$\frac{π \cdot 25}{3} \cdot (3 \cdot 4)$

Rewrite the expression.

$π \cdot 25 \cdot 4$

Step 7

Simplify the expression.

Multiply $4$ by $25$ .

$π \cdot 100$

Move $100$ to the left of $π$ .

$100 π$

Step 8

The result can be shown in multiple forms.

Exact Form:

$100 π$

Decimal Form:

$314.15926535 \dots$

Find the Volume cone (12)(5)

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