The volume of a sphere is 72 m3. 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)

Question

m^3

Answer 1

The volume of a sphere is given by the formula V = (4/3) * π * r^3, where V is the volume and r is the radius.

Given that the volume of the sphere is 72 m^3, we can rearrange the formula to solve for the radius:

72 = (4/3) * π * r^3

Dividing both sides by (4/3) * π, we get:

r^3 = 72 / ((4/3) * π)

To find the volume of the cone, we can use the formula V = (1/3) * π * r^2 * h, where V is the volume, r is the radius, and h is the height.

Since the radius of the cone is the same as the sphere's radius, we can substitute r^3 into the formula for the cone's volume:

V_cone = (1/3) * π * (r^3)^2 * h

V_cone = (1/3) * π * r^6 * h

The height of the cone is equal to the sphere's diameter, which is 2 * r. Substituting this into the formula, we get:

V_cone = (1/3) * π * r^6 * (2 * r)

V_cone = (2/3) * π * r^7

Since r^3 = 72 / ((4/3) * π), we can substitute this value into the formula for the cone's volume:

V_cone = (2/3) * π * (72 / ((4/3) * π))^7

Simplifying the expression, we get:

V_cone ≈ 2.034 * 10^33 m^3

Therefore, the volume of the cone is approximately 2.034 * 10^33 m^3.