The value of the sphere is 72M to the third power. What is the volume of the cone if the radius is the same as the spheres, and the height is equal to the spears diameter?

Answer 1

To find the volume of the cone, we need to know the radius and height of the cone, which are given to be the same as the sphere.

The volume of a sphere is given by the formula:

V_sphere = (4/3) * π * r^3

Here, we have V_sphere = 72M to the third power. Let's represent this in terms of units:

V_sphere = 72 M^3

To find the radius of the sphere (and consequently the cone), we need to solve for r in the sphere volume formula:

72 M^3 = (4/3) * π * r^3

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

r^3 = (72 M^3) / [(4/3) * π]

Now, let's find the value of r:

r^3 = (3 * 72 M^3) / (4 * π)
r^3 = (3 * 72) / (4 * π) M^3 [Canceling out the units]

r^3 ≈ 54.548 M^3

Taking the cube root of both sides, we find:

r ≈ 3.736 M

Now, the height of the cone is given as equal to the sphere's diameter. The diameter of the sphere is twice the radius, so the height of the cone is:

height = 2 * r
height ≈ 2 * 3.736 M
height ≈ 7.472 M

Now, we can use the formula for the volume of a cone to find the volume:

V_cone = (1/3) * π * r^2 * height

Substituting the values, we get:

V_cone = (1/3) * π * (3.736 M)^2 * 7.472 M

Evaluating this expression, we find:

V_cone ≈ 109.181 M^3

Therefore, the volume of the cone is approximately 109.181 cubic meters.