The volume of a sphere is given by the formula V = 4/3πr3, where r is the radius of the sphere. Which of the following gives the radius of the sphere in terms of the volume of the sphere?

Explanation

To find the radius in terms of the volume, start with the formula for the volume of a sphere: V = 4/3πr3. Rearrange the equation to solve for r3 by dividing both sides by 4/3π, yielding r3 = 3V⁄4π. Finally, take the cube root of both sides to solve for r, giving r = ³√3V⁄4π. Thus, option D is correct. The other options either incorrectly rearrange the formula or misunderstand the mathematical operations needed to isolate r.