Question

question 10 of 10
solve the equation ( x = \frac{2}{3}pi r^3 ) for ( r ).

a. ( r = sqrt3{3x - 2pi} )

b. ( r = sqrt3{3x(2pi)} )

c. ( r = sqrt3{\frac{2pi}{3x}} )

d. ( r = sqrt3{\frac{3x}{2pi}} )

Explanation:

Step1: Isolate the $r^3$ term

Multiply both sides by $\frac{3}{2\pi}$:
$$r^3 = \frac{3x}{2\pi}$$

Step2: Solve for $r$

Take cube root of both sides:
$$r = \sqrt[3]{\frac{3x}{2\pi}}$$

Answer:

D. $r = \sqrt[3]{\frac{3x}{2\pi}}$