Question

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

Answer 1

[AI-generated answer — Bot GPT 3.5]

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

Given that the volume of the sphere is 72 m^3, we can set up the equation as follows:
72 = (4/3)πr^3
To find the radius of the sphere, we can rearrange the equation:
r^3 = (3/4)(72/π)
r^3 = 54/π
r = (54/π)^(1/3) (approximately 2.76 meters)
Now, let's find the height of the cone using the given information:
The height of the cone is equal to the sphere's diameter, so it is twice the radius:
height = 2r = 2 * 2.76 = 5.52 meters
The volume of a cone is given by the formula V = (1/3)πr^2h, where r is the radius and h is the height of the cone.
Plugging in the values we found:
V = (1/3)π * 2.76^2 * 5.52 ≈ 33 m^3
Therefore, the volume of the cone is approximately 33 m^3.