Question

the volume of a sphere is 72 m^3 what is the volume of a cone that shares the same radius and has a height equal to the spheres diameter?

Answer 1

wrong

Answer 2

To find the volume of the cone, we need to first find the radius and height of the sphere.

Since the volume of the sphere is given as 72 m^3, we have:

(Volume of Sphere) = (4/3)πr^3 = 72

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

r^3 = (72 * 3)/(4π)
r^3 ≈ 54.62
r ≈ ∛54.62
r ≈ 3.82 m (approx.)

Now, let's find the sphere's diameter:

Diameter = 2 * Radius = 2 * 3.82 m = 7.64 m

The height of the cone is equal to the sphere's diameter, so it is 7.64 m.

The formula for the volume of a cone is:

Volume of Cone = (1/3)πr^2h

Substituting the known values, we have:

Volume of Cone = (1/3)π * (3.82)^2 * 7.64
Volume of Cone ≈ 83.72 m^3

Therefore, the volume of the cone that shares the same radius and has a height equal to the sphere's diameter is approximately 83.72 m^3.

Answer 3

Apologies for the mistake in my previous response.

Let's compute the correct values:

Given that the volume of the sphere is 72 m^3, we can use the formula for the volume of a sphere to find the radius:

(Volume of Sphere) = (4/3)πr^3
72 = (4/3)πr^3

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

r^3 = (72 * 3)/(4π)
r^3 = 54/π
r ≈ ∛(54/π)
r ≈ 2.51 m (approx.)

Now, let's find the sphere's diameter:

Diameter = 2 * Radius = 2 * 2.51 m = 5.02 m

The height of the cone is equal to the sphere's diameter, so it is 5.02 m.

The formula for the volume of a cone is:

Volume of Cone = (1/3)πr^2h

Substituting the known values, we have:

Volume of Cone = (1/3)π * (2.51)^2 * 5.02
Volume of Cone ≈ 10.53 m^3

Therefore, the volume of the cone that shares the same radius and has a height equal to the sphere's diameter is approximately 10.53 m^3.