Question

Two cylinders have equal diameters. are their volumes also equal? is the same true for cones and spheres?

Answer 1

are their volumes also equal?
Not necessarily, if they have the same height the volume of the two cylinders is the same. However, if they do not have the same height, the volume is different. The volume of a cylinder is:
V = pi * r ^ 2 * h.
the same true for cones and spheres?
For the cone, the same thing happens with the cylinder. It will depend on the height. The volume of the cone is:
V = (1/3) * pi * r ^ 2 * h.
For a sphere YES. the volumes are equal if they have the same diameter since their equation depends only on the radius. The volume of the sphere is:
V = (4/3) * pi * r ^ 3

Answer 2

Although two cylinders may have equal diameters, their volumes are not necessarily equal, as the volume of a cylinder is dependent also on the cylinder's height. The same holds true for cones. Spheres, however, are, by nature, proportional. Therefore, if two spheres have the same diameter, they also have the same volumes.