Answer :
To solve for [tex]\( r \)[/tex] from the formula for the volume of a sphere, [tex]\( V = \frac{4}{3} \pi r^3 \)[/tex], follow these steps:
1. Start with the given equation:
[tex]\[ V = \frac{4}{3} \pi r^3 \][/tex]
2. Isolate [tex]\( r^3 \)[/tex]:
To do this, multiply both sides of the equation by [tex]\( \frac{3}{4\pi} \)[/tex] to cancel out the coefficient on the right side.
[tex]\[ \frac{3V}{4\pi} = r^3 \][/tex]
3. Solve for [tex]\( r \)[/tex]:
Take the cube root of both sides to solve for [tex]\( r \)[/tex].
[tex]\[ r = \sqrt[3]{\frac{3V}{4\pi}} \][/tex]
Thus, the formula solved for [tex]\( r \)[/tex] is:
[tex]\[ r = \sqrt[3]{\frac{3V}{4\pi}} \][/tex]
Therefore, the correct choice from the options given is:
[tex]\[ r = \sqrt[3]{\frac{3V}{4\pi}} \][/tex]
1. Start with the given equation:
[tex]\[ V = \frac{4}{3} \pi r^3 \][/tex]
2. Isolate [tex]\( r^3 \)[/tex]:
To do this, multiply both sides of the equation by [tex]\( \frac{3}{4\pi} \)[/tex] to cancel out the coefficient on the right side.
[tex]\[ \frac{3V}{4\pi} = r^3 \][/tex]
3. Solve for [tex]\( r \)[/tex]:
Take the cube root of both sides to solve for [tex]\( r \)[/tex].
[tex]\[ r = \sqrt[3]{\frac{3V}{4\pi}} \][/tex]
Thus, the formula solved for [tex]\( r \)[/tex] is:
[tex]\[ r = \sqrt[3]{\frac{3V}{4\pi}} \][/tex]
Therefore, the correct choice from the options given is:
[tex]\[ r = \sqrt[3]{\frac{3V}{4\pi}} \][/tex]
