### Instruction: The diameter of a cone is 30 decimeters. If the height is two times the radius, what is the volume of the cone in cubic decimeters?### Response: The volume of a cone is given by the formula V = (1/3)πr^2h, where r is the radius and h is the height.
The diameter is 30 decimeters, so the radius is half of that, or 15 decimeters.
The height is two times the radius, so the height is 2 * 15 = 30 decimeters.
Substituting these values into the formula, we get V = (1/3)π(15)^2(30) = (1/3)π * 225 * 30.
Simplifying, we get V = 2250π cubic decimeters.