A cylinder of base radius 2x and height 3x has the same volume as a cone of base radius 3x and height h. Find h in terms of x.

The equation for the volume of a cylinder is (1/2)pi(r²)*H, where r is the radius and H is the height of the cylinder. For the cylinder given, the volume is therefore (1/2)pi((2x)²)*3x, or more simply: 6x³*pi. The equation for the volume of a cone is (1/3)pi((r²)*H, where r is again the radius and H is again the height of the cone. For the cone given, the volume is therefore (1/3)pi((3x)²)*h, or more simply: 3x²pih. Since the volume of the cylinder is equal to the volume of the cone, we can say that:6x³*pi = 3x²pih. By dividing both sides of the equation by pi, and then both sides of the equation by 3x², we can determine that h=2x.