in order for the ratio of the volumes to be true what measurements would have to be equal in all 3 solide: cone, sphere, and cylinder

In order for the ratio of the volumes of a cone, sphere, and cylinder to be true, the heights of the cone and cylinder would have to be equal. This is because the volume of a cone and cylinder are both directly proportional to their respective heights.

Additionally, the radius of the cone and cylinder would have to be equal to the radius of the sphere. This is because the volume of a sphere is directly proportional to the cube of its radius, while the volume of a cylinder or cone is directly proportional to the square of its radius.

Therefore, for the ratio of the volumes of a cone, sphere, and cylinder to be true, the heights of the cone and cylinder would have to be equal, and the radius of the cone and cylinder would have to be equal to the radius of the sphere.