Basic Math Examples



\begin{matrix} h = & 12 r = & 8 \end{matrix}

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

Step 1

The volume of a cone is equal to

\frac{1}{3}

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

π r^{2}

$π r^{2}$ times the height

h

$h$ .

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

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

Step 2

Substitute the values of the radius

r = 8

$r = 8$ and height

h = 12

$h = 12$ into the formula to find the volume of the cone. Pi

π

$π$ is approximately equal to

3.14

$3.14$ .

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

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

Step 3

Combine

\frac{1}{3}

$\frac{1}{3}$ and

π

$π$ .

\frac{π}{3} \cdot 8^{2} \cdot 12

$\frac{π}{3} \cdot 8^{2} \cdot 12$

Step 4

Raise

8

$8$ to the power of

2

$2$ .

\frac{π}{3} \cdot 64 \cdot 12

$\frac{π}{3} \cdot 64 \cdot 12$

Step 5

Combine

\frac{π}{3}

$\frac{π}{3}$ and

64

$64$ .

\frac{π \cdot 64}{3} \cdot 12

$\frac{π \cdot 64}{3} \cdot 12$

Step 6

Cancel the common factor of

3

$3$ .

Tap for more steps...

Step 6.1

Factor

3

$3$ out of

12

$12$ .

\frac{π \cdot 64}{3} \cdot (3 (4))

$\frac{π \cdot 64}{3} \cdot (3 (4))$

Step 6.2

Cancel the common factor.

$\frac{π \cdot 64}{3} \cdot (3 \cdot 4)$

Step 6.3

Rewrite the expression.

$π \cdot 64 \cdot 4$

Step 7

Simplify the expression.

Tap for more steps...

Step 7.1

Multiply

$4$ by

$64$ .

$π \cdot 256$

Step 7.2

Move

$256$ to the left of

$π$ .

$256 π$

Step 8

The result can be shown in multiple forms.

Exact Form:

$256 π$

Decimal Form:

$804.24771931 \dots$