What is 1/3 pi(30)^2(30) ?

The solution to 1/3 pi(30)^2(30) is 9000pi

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simplify 1/3 pi(30)^2(30)

simplify

\frac{1}{3} π (30)^{2} (30)

9000 π

Decimal Notation

28274.33388 \dots

Solution steps

\frac{1}{3} π (30)^{2} (30)

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

3 0^{2} \cdot 30 = 3 0^{2 + 1}

= \frac{1}{3} π 3 0^{2 + 1}

Add the numbers:

2 + 1 = 3

= \frac{1}{3} π 3 0^{3}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 π 3 0 ^{3}}{3}

Multiply:

1 π = π

= \frac{3 0 ^{3} π}{3}

Factor

3 0^{3} : 2^{3} \cdot 3^{3} \cdot 5^{3}

= \frac{2 ^{3} \cdot 3 ^{3} \cdot 5 ^{3} π}{3}

Cancel the common factor:

3

= 2^{3} \cdot 5^{3} \cdot 3^{2} π

2^{3} = 8

= 5^{3} \cdot 3^{2} \cdot 8 π

5^{3} = 125

= 3^{2} \cdot 8 \cdot 125 π

3^{2} = 9

= 8 \cdot 125 \cdot 9 π

Multiply the numbers:

8 \cdot 125 \cdot 9 = 9000

= 9000 π

e^{- x} \frac{( 1 - cos ( x ) )}{x}

3.33 \cdot 1 0^{- 6}

\frac{1}{a} e^{- (\frac{2}{3} (- 3)^{2})}

2.05 \cdot 85 0^{- 0.18}

e^{2 t} e^{2 t}