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.
GF
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