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?
Correct answer: D. 3√3V/4π
- A. r = 4π⁄3V
- B. r = 3V⁄4π
- C. r = 3√4π⁄3V
- D. 3√3V/4π
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.
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