an image shows a cone, a sphere and a cylinder. in order for the ratio of volumes 1 : 2 : 3 to be true, what measurements would have to be equal in all 3 solids?
In order for the ratio of volumes to be 1:2:3, the measurements that would have to be equal in all three solids would be the height.
If the height of the cone, sphere, and cylinder were all equal, then the volume of the cone would be 1/3πr^2h, the volume of the sphere would be 4/3πr^3, and the volume of the cylinder would be πr^2h.
Therefore, the ratio of volumes would be (1/3πr^2h) : (4/3πr^3) : (πr^2h), which simplifies to 1:2:3.