The volume of a sphere is 72 m3
sphere's diameter? (1 point)
• What is the volume of a cone if its radius is the same as the sphere's and its height is equal to the
Let's start by finding the radius of the sphere.
Volume of a sphere formula:
V = (4/3) * π * r^3
Given that the volume is 72 m^3, we can plug that in and solve for the radius:
72 = (4/3) * π * r^3
r^3 = (72 * 3) / (4 * π)
r^3 = 54 / π
r = ∛(54 / π) ≈ 2.7802 meters
Now let's find the diameter of the sphere:
Diameter = 2 * radius
Diameter = 2 * 2.7802
Diameter ≈ 5.5604 meters
For the cone, if the radius is the same as the sphere's and the height is equal to the radius, then the cone's height will also be 2.7802 meters. Let's find the volume of the cone.
Volume of a cone formula:
V = (1/3) * π * r^2 * h
Plugging in the values:
V = (1/3) * π * (2.7802)^2 * 2.7802
V = (1/3) * π * 22.0411 * 2.7802
V = (1/3) * π * 61.3036
V ≈ 64.3376 m^3
Therefore, the diameter of the sphere is approximately 5.56 meters and the volume of the cone is approximately 64.34 m^3.