Question

The volume of a sphere is 72 m^3 . What is the volume of a cone if its radius is the same as the sphere’s and its height is equal to the sphere’s diameter?(1 point)

Answer 1

[AI-generated answer — Bot GPT 3.5]

The volume of a cone is given by the formula: V = (1/3)πr^2h, where V is the volume, π is approximately 3.14, r is the radius, and h is the height.

In this case, we are given that the radius of the cone is the same as the sphere, so the radius of the cone is √(72/π). We are also given that the height of the cone is equal to the sphere's diameter, so the height of the cone is 2√(72/π).

To find the volume of the cone, we can substitute these values into the formula:

V = (1/3)π(√(72/π))^2(2√(72/π))
= (1/3)π(72/π)(2√(72/π))
= (1/3)(72)(2)
= 48 m^3

Therefore, the volume of the cone is 48 m^3.