suppose a sphere and a cone share the same radius and the height of the cone is twice the radius. nich ratio describes the relationship between the formulas for the volume of a cone to the volume of a nere? (1 point)

Answer 1

The Nic ratio, also known as the volume ratio, describes the relationship between the volumes of the cone and the sphere.

The volume of a cone can be calculated using the formula Vc = 1/3 * π * r^2 * h, where r is the radius of the cone and h is the height of the cone. In this case, since the height of the cone is twice the radius, we can substitute h = 2r into the formula to get Vc = 1/3 * π * r^2 * (2r) = 2/3 * π * r^3.

The volume of a sphere can be calculated using the formula Vs = 4/3 * π * r^3, where r is the radius of the sphere.

Comparing the formulas, we can see that the volume of the cone Vc is 2/3 times the volume of the sphere Vs, or Vc/Vs = 2/3.

Therefore, the Nic ratio or volume ratio between the formulas for the volume of a cone to the volume of a sphere is 2/3.