The formula for the volume of a right cone is V = (1/3)πr^2h, where r is the radius and h is the height.
We are given that V = 252π/3 and h = 21. Substituting these values in the formula, we get:
252π/3 = (1/3)πr^2(21)
Canceling the 3's and π on both sides, we get:
84 = 7r^2
Dividing both sides by 7, we get:
r^2 = 12
Taking the square root of both sides, we get:
r = √12 = 2√3
Therefore, the radius of the cone is 2√3 units.