the formula for the volume of a sphere is $v = \\frac{4}{3}\\pi r^{3}$. what is the formula solved for…

the formula for the volume of a sphere is $v = \\frac{4}{3}\\pi r^{3}$. what is the formula solved for $r$?\n$r = 3v + 4\\pi$\n$r=sqrt3{3v - 4\\pi}$\n$r=sqrt3{\\frac{3v}{4\\pi}}$\n$r^{3}=3v - 4\\pi$

the formula for the volume of a sphere is $v = \\frac{4}{3}\\pi r^{3}$. what is the formula solved for $r$?\n$r = 3v + 4\\pi$\n$r=sqrt3{3v - 4\\pi}$\n$r=sqrt3{\\frac{3v}{4\\pi}}$\n$r^{3}=3v - 4\\pi$

Answer

Explanation:

Step1: Isolate $r^{3}$

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

Step2: Solve for $r$

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

Answer:

$r=\sqrt[3]{\frac{3V}{4\pi}}$ (corresponding to the third option in the multiple - choice list)