Question

solve the equation ( x = \frac{4}{3}pi r^3 ) for ( r ).

a. ( r = sqrt3{\frac{3x}{4pi}} )

b. ( r = sqrt3{3x - 4pi} )

c. ( r = sqrt3{\frac{4pi}{3x}} )

d. ( r = sqrt3{3x(4pi)} )

Explanation:

Step1: Isolate $\pi r^3$ term

Multiply both sides by 3:
$3x = 4\pi r^3$

Step2: Isolate $r^3$ term

Divide both sides by $4\pi$:
$r^3 = \frac{3x}{4\pi}$

Step3: Solve for $r$

Take cube root of both sides:
$r = \sqrt[3]{\frac{3x}{4\pi}}$

Answer:

A. $r = \sqrt[3]{\frac{3x}{4\pi}}$