Which option most correctly describes the relationship between the formulas for the volumes of cylinders to that of spheres and cones, assuming the diameter of the sphere is equal to the height of both the cylinder and the cone? (1 point) Responses A The volume of a cylinder is equal to the difference of the volume of a sphere and a cone. B The volume of a cylinder is equal to the difference of the volume of a sphere and a cone. C The volume of a cylinder is double the volume of a sphere. The volume of a cylinder is double the volume of a sphere. D The volume of a cylinder is double the volume of a cone. The volume of a cylinder is double the volume of a cone. The volume of a cylinder is equal to the sum of the volume of a sphere and a cone.

Question

GPT 3.5 · Answer

The correct option would be D. The volume of a cylinder is double the volume of a cone. The volume of a cylinder is equal to the sum of the volume of a sphere and a cone. This is because both the sphere and the cone have the same height and diameter as the cylinder, and the volume of a sphere is equal to (4/3)πr^3, and the volume of a cone is equal to (1/3)πr^2h, where r is the radius and h is the height.