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? bot
To find the volume of a cone, we need to know its radius and height.
Given that the radius of the cone is the same as the sphere, we can use the formula for the volume of a sphere to find the radius. The formula for the volume of a sphere is:
V = (4/3) * π * r^3
We are given that the volume of the sphere is 72 m3, so we can write the equation as:
72 = (4/3) * π * r^3
Now, we can solve for the radius of the sphere:
r^3 = (72 * 3) / (4π)
r^3 = 54 / π
r ≈ 3.88 m
Now, since the height of the cone is equal to the sphere's diameter, we can use the radius we just found to calculate the height of the cone:
Height = 2 * r
Height ≈ 2 * 3.88 m
Height ≈ 7.76 m
Finally, we can use the formula for the volume of a cone to find the volume of the cone:
V = (1/3) * π * r^2 * h
V = (1/3) * π * (3.88^2) * 7.76
V ≈ 116.74 m3
So, the volume of the cone is approximately 116.74 m3.
wrong
Apologies for the mistake. Let me correct it:
We are given that the volume of the sphere is 72 m³. The formula for the volume of a sphere is:
V = (4/3) * π * r^3
To find the radius of the sphere, we can rearrange the formula as:
r^3 = (3V) / (4π)
r^3 = (3 * 72) / (4π)
r^3 = 54 / π
r ≈ 3.86 m
Since the radius of the cone is the same as the sphere's radius, the radius of the cone is approximately 3.86 m.
Now, given that the height of the cone is equal to the diameter of the sphere, which is twice the radius, the height of the cone is approximately 2 * 3.86 m = 7.72 m.
Next, we can use the formula for the volume of a cone to find the volume of the cone:
V_cone = (1/3) * π * r^2 * h
V_cone = (1/3) * π * (3.86^2) * 7.72
V_cone ≈ 100.90 m³
Therefore, the volume of the cone is approximately 100.90 m³.