Question

question 3 of 25 a solid sphere is cut into 3 equal wedges. the volume of each wedge is v = 4/9 πr³. solve the formula for r. a. r = ∛(9v(4π)) b. r = ∛(9v/4π) c. r = ∛(9v - 4π) d. r = ∛(4π/9v)

Explanation:

Step1: Isolate $r^3$

Given $V = \frac{4}{9}\pi r^{3}$, multiply both sides by $\frac{9}{4\pi}$ to get $r^{3}=\frac{9V}{4\pi}$.
$r^{3}=\frac{9V}{4\pi}$

Step2: Solve for $r$

Take the cube - root of both sides. So $r=\sqrt[3]{\frac{9V}{4\pi}}$.

Answer:

B. $r = \sqrt[3]{\frac{9V}{4\pi}}$