The volume of a right cone is 343π units^3. If its height is 21 units, find the circumference in terms of π.
The formula for the volume of a cone is given by V = (1/3)πr^(2)h, where V is the volume, r is the radius of the base, and h is the height.
Since the volume is given as 343π units^(3) and the height is given as 21 units, we can rearrange the formula to solve for the radius:
343π = (1/3)πr^(2)(21)
Multiplying both sides by 3 and dividing both sides by 21π gives:
r^(2) = (343π * 3)/(21π) = 49
Taking the square root of both sides gives:
r = √(49) = 7
The circumference of the base of a cone is given by C = 2πr.
Therefore, the circumference of the base of this cone is:
C = 2π * 7 = 14π units. Answer: \boxed{14 \pi}.