Basic Math Examples

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\begin{matrix} h = & 24 r = & 7 \end{matrix}

$\begin{array}{r} h = & 24 \\ r = & 7 \end{array}$

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 = 7

$r = 7$ and height

h = 24

$h = 24$ 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 7^{2} \cdot 24

$\frac{1}{3} \cdot π \cdot 7^{2} \cdot 24$

Step 3

Combine

\frac{1}{3}

$\frac{1}{3}$ and

π

$π$ .

\frac{π}{3} \cdot 7^{2} \cdot 24

$\frac{π}{3} \cdot 7^{2} \cdot 24$

Step 4

Raise

7

$7$ to the power of

2

$2$ .

\frac{π}{3} \cdot 49 \cdot 24

$\frac{π}{3} \cdot 49 \cdot 24$

Step 5

Combine

\frac{π}{3}

$\frac{π}{3}$ and

49

$49$ .

\frac{π \cdot 49}{3} \cdot 24

$\frac{π \cdot 49}{3} \cdot 24$

Step 6

Cancel the common factor of

3

$3$ .

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Step 6.1

Factor

3

$3$ out of

24

$24$ .

\frac{π \cdot 49}{3} \cdot (3 (8))

$\frac{π \cdot 49}{3} \cdot (3 (8))$

Step 6.2

Cancel the common factor.

$\frac{π \cdot 49}{3} \cdot (3 \cdot 8)$

Step 6.3

Rewrite the expression.

$π \cdot 49 \cdot 8$

Step 7

Simplify the expression.

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Step 7.1

Multiply

$8$ by

$49$ .

$π \cdot 392$

Step 7.2

Move

$392$ to the left of

$π$ .

$392 π$

Step 8

The result can be shown in multiple forms.

Exact Form:

$392 π$

Decimal Form:

$1231.50432020 \dots$