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 and its height is equal to the Spheres diameter?

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the volume of a cone, we need to know the radius (r) and height (h) of the cone. In this case, the radius of the cone is the same as the sphere and the height is equal to the sphere's diameter.

Given that the volume of the sphere is 72 m³, we can use the formula for the volume of a sphere to find the radius (r) and substitute it into the formula for the volume of a cone.

The formula for the volume of a sphere is:
V_sphere = (4/3)πr³

So, we can rearrange the formula to solve for the radius (r):
r = ∛(3V_sphere / 4π)

Plugging in the volume of the sphere (V_sphere = 72 m³) into the formula, we have:
r = ∛(3*72 / 4π)
r = ∛(216 / 4π)
r ≈ ∛(54 / π)
r ≈ ∛17.17
r ≈ 2.66

Now that we have the radius of the cone (r ≈ 2.66), we can calculate its height (h) using the given information that the height is equal to the sphere's diameter.

Diameter of the sphere = 2 * radius of the sphere = 2 * 2.66 = 5.32

Hence, the height (h) of the cone is equal to 5.32 m.

Finally, we can calculate the volume of the cone using the formula:
V_cone = (1/3)πr²h

Plugging in the values, we have:
V_cone = (1/3)π * (2.66)^2 * 5.32
V_cone ≈ 9.45 m³

Therefore, the volume of the cone is approximately 9.45 m³.