A sphere and a right circular cylinder have identical radii, and their volumes are equal. What is the height of the cylinder in terms of its radius?

Explanation

Given that the sphere and cylinder share the same radius and have equal volumes, we set their volume formulas equal: Volume of sphere = (4/3)πr³ and volume of cylinder = πr²h. Equating gives (4/3)πr³ = πr²h, which simplifies to h = (4/3)r. Therefore, the height of the cylinder is four-thirds of its radius.