answer this wuestion

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? (1 point)
Check

Answer 1

To find the volume of the cone, we need to use the formula:

Volume of a cone = (1/3) * π * r^2 * h

Given that the radius of the cone is the same as the sphere's, we can calculate it as:
r = (diameter of sphere) / 2

Since the height of the cone is equal to the sphere's diameter, we have:
h = (diameter of sphere)

Substituting these values into the formula, we get:

Volume of cone = (1/3) * π * (diameter of sphere / 2)^2 * (diameter of sphere)

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

Volume of sphere = (4/3) * π * r^3

Given that the volume of the sphere is 72 m^3, we can solve for the radius as follows:

72 = (4/3) * π * r^3

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

r^3 = 72 / ((4/3) * π)

Simplifying further:

r^3 = (72 * 3) / (4 * π)

r^3 = 54 / π

Taking the cubic root of both sides:

r = (54 / π)^(1/3)

Now we can substitute this value for the radius and the diameter of the sphere into the formula for the volume of the cone:

Volume of cone = (1/3) * π * [(54 / π)^(1/3) / 2)^2 * (54 / π)^(1/3)

Simplifying further:

Volume of cone = (1/3) * π * (54 / (2π))^[2/3] * (54 / π)^[1/3]

This calculation is difficult to perform without a calculator.