Question

The volume of a sphere is 72m to the 3rd power . What is the volume of a cone if it’s radius is the same as the sphere and it’s height is equal to the sphere diatmeter

Answer 1

To find the volume of a cone, we can use the formula:

V = (1/3) * π * r^2 * h

Given that the radius of the cone is the same as the radius of the sphere, and the height of the cone is equal to the diameter of the sphere, we can substitute these values into the formula.

First, let's find the radius and height of the sphere:

Sphere radius = r
Sphere height = 2 * r (diameter = 2 * radius)

The volume of the sphere is given as 72 m^3, so:

72 = (4/3) * π * r^3

To find r, we can rearrange the equation:

(4/3) * π * r^3 = 72
r^3 = (72 * 3) / (4 * π)
r^3 = 54 / π
r = (54 / π)^(1/3)

Now, let's substitute these values into the volume formula for the cone:

V = (1/3) * π * r^2 * h
V = (1/3) * π * [(54 / π)^(1/3)]^2 * (2 * [(54 / π)^(1/3)])

Simplifying the equation, we get:

V = (1/3) * π * (54 / π)^(2/3) * (2 * (54 / π)^(1/3))^3
V = (1/3) * π * 54^(2/3) * (2^3 * (54 / π)^(1/3))^3
V = (1/3) * π * 54^(2/3) * (8 * (54 / π)^(1/3))^3
V = (1/3) * π * 54^(2/3) * (8 * 54^(1/3))⁻³
V = (1/3) * π * 54^(2/3) * (8 * 54^(1/3))⁻³

Using a calculator, we can compute this value:

V ≈ 259.908 m^3

Therefore, the volume of the cone is approximately 259.908 cubic meters.