Question

Solve the equation x=5/3 pi r ^3 A. B C D?

Answer 1

Answer:

B (3x / ( 5pi)) ^ 1/3 =  r

Step-by-step explanation:

x=5/3 pi r ^3

Multiply each side by 3/5

3/5 x= pi r ^3

Divide each side by pi

3x / ( 5pi) = pi r^3 /pi

3x / ( 5pi) =  r^3

Take the cube root of each side

(3x / ( 5pi)) ^ 1/3 =  r^3 ^ 1/3

(3x / ( 5pi)) ^ 1/3 =  r

Answer 2

How to solve?

Here, we just have to express r in terms of x when we are provided with the relation between x and r. We have to flip and sent it to the Right hand side.

Solution:

We have,

• $\large{ \rm{x = \frac{5}{3} \pi {r}^{3} }}$

Solving it further,

$\large{ \longrightarrow{ \rm{x = \frac{5}{3} \pi {r}^{3} }}}$

Taking 5/3 to the other side by dividing it,

$\large{ \longrightarrow{ \rm{ \frac{3x}{5} = \pi {r}^{3} }}}$

Now, taking π to the other side by dividing it,

$\large{ \longrightarrow{ \rm{ \frac{3x}{5\pi} = {r}^{3} }}}$

Cube rooting LHS to get r

$\large{ \longrightarrow{ \rm{ \sqrt[3]{ \frac{3x}{5\pi} } = r}}}$

Flipping it,

$\large{ \longrightarrow{ \rm{r = \sqrt[3]{ \frac{3x}{5\pi} } }}}$

So, the correct option:

$\huge{ \boxed{ \bf{ \red{Option \: B}}}}$

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