What are the solutions to the equation 400= 4/3 pir^3 ?

The solutions to the equation 400= 4/3 pir^3 are

Find the zeros of 400= 4/3 pir^3

The zeros of 400= 4/3 pir^3 are

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400 = \frac{4}{3} π r^{3}

r = 3 \frac{300}{π}, r = - \frac{3 300 π ^{\frac{2}{3}}}{2 π} + i \frac{3 ^{\frac{5}{6}} 3 100 π ^{\frac{2}{3}}}{2 π}, r = - \frac{3 300 π ^{\frac{2}{3}}}{2 π} - i \frac{3 ^{\frac{5}{6}} 3 100 π ^{\frac{2}{3}}}{2 π}

Solution steps

400 = \frac{4}{3} π r^{3}

Switch sides

\frac{4}{3} π r^{3} = 400

Simplify

\frac{4}{3} π : \frac{4 π}{3}

\frac{4 π}{3} r^{3} = 400

Multiply both sides by

3

4 π r^{3} = 1200

Divide both sides by

4 π

r^{3} = \frac{300}{π}

For

x^{3} = f (a)

the solutions are

x = 3 f (a), 3 f (a) \frac{- 1 - 3 i}{2}, 3 f (a) \frac{- 1 + 3 i}{2}

r = 3 \frac{300}{π}, r = 3 \frac{300}{π} \frac{- 1 + 3 i}{2}, r = 3 \frac{300}{π} \frac{- 1 - 3 i}{2}

Simplify

3 \frac{300}{π} \frac{- 1 + 3 i}{2} : - \frac{3 300 π ^{\frac{2}{3}}}{2 π} + i \frac{3 ^{\frac{5}{6}} 3 100 π ^{\frac{2}{3}}}{2 π}

Simplify

3 \frac{300}{π} \frac{- 1 - 3 i}{2} : - \frac{3 300 π ^{\frac{2}{3}}}{2 π} - i \frac{3 ^{\frac{5}{6}} 3 100 π ^{\frac{2}{3}}}{2 π}

r = 3 \frac{300}{π}, r = - \frac{3 300 π ^{\frac{2}{3}}}{2 π} + i \frac{3 ^{\frac{5}{6}} 3 100 π ^{\frac{2}{3}}}{2 π}, r = - \frac{3 300 π ^{\frac{2}{3}}}{2 π} - i \frac{3 ^{\frac{5}{6}} 3 100 π ^{\frac{2}{3}}}{2 π}

3 x^{4} + x^{2} - 4 = 0

x^{3} = 3 x + 2

2 x (x + 10) (x^{2} + 49) = 0

- a^{3} + 3 a + 2 = 0

2 x - x^{3} = 0

What are the solutions to the equation 400= 4/3 pir^3 ?
The solutions to the equation 400= 4/3 pir^3 are
Find the zeros of 400= 4/3 pir^3
The zeros of 400= 4/3 pir^3 are