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?
nope
Given that the volume of the sphere is 72 m³, we can find the radius of the sphere using the formula for the volume of a sphere.
Let's denote the radius of the sphere as r. The volume of the sphere is given by the formula:
V_sphere = (4/3) * π * r^3
We can rearrange the formula to solve for the radius:
r^3 = (3/4 * V_sphere) / π
r^3 = (3/4 * 72) / π
r^3 ≈ 162 / π
r ≈ ∛(162 / π)
r ≈ 5.185 m
Since the cone's radius is the same as the sphere's, the radius of the cone is also approximately 5.185 m.
The height of the cone is equal to the sphere's diameter, which is twice the radius of the sphere:
Height_cone = 2 * r
Height_cone = 2 * 5.185 m
Height_cone ≈ 10.37 m
The formula for the volume of a cone is given by:
V_cone = (1/3) * π * r^2 * h
where r is the radius and h is the height of the cone.
Substituting the values, we have:
V_cone = (1/3) * π * (5.185 m)^2 * 10.37 m
V_cone ≈ 283.07 m³
Therefore, the volume of the cone is approximately 283.07 m³.