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?
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.
wrong
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.