Suppose a sphere and a cone share the same radius and the same height, which is twice the radius. Which ratio describes the relationship between the formulas for the volume of a cone to the volume of a cylinder?
The volume of a cone is given by the formula Vcone = (1/3)πr²h, where r is the radius and h is the height.
In this case, the radius of the cone and the radius of the sphere are the same, so we can also say that the radius of the cone is equal to the radius of the sphere.
The volume of the sphere is given by the formula Vsphere = (4/3)πr³, where r is the radius.
The height of the cone is twice the radius, so we can write h = 2r.
To find the ratio between the volume of the cone and the volume of the sphere, we can divide the volume of the cone by the volume of the sphere:
Ratio = (1/3)πr²(2r) / (4/3)πr³
= (2/3)πr³ / (4/3)πr³
= 2/4
= 1/2
Therefore, the ratio describing the relationship between the formulas for the volume of a cone to the volume of a sphere is 1/2.