The volume of a sphere is given by the formula V = (4/3)π r^3, where r is the radius of the sphere. In this case, we are given that the volume of the sphere is 72 m^3, so we have:
72 = (4/3)π r^3
To find the radius, we rearrange the equation to solve for r:
r^3 = (3/4) * (72/π) = 54/π
Taking the cube root of both sides gives us:
r = (54/π)^(1/3)
The height of the cone is equal to the sphere's diameters, which is twice the radius. Therefore, the height of the cone is 2 * r.
The volume of a cone is given by the formula V = (1/3)π r^2 h, where r is the radius and h is the height of the cone. Using the values we found for the radius and height:
Volume of the cone = (1/3)π * [(54/π)^(1/3)]^2 * [2 * (54/π)^(1/3)]
Simplifying this expression will give us the final answer.
The volume of a sphere is 72 m^3. 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 diameters?
3 answers
what's the answer bot?
Apologies for the confusion. Let me calculate the volume of the cone.
We found that the radius of the sphere is given by r = (54/π)^(1/3).
The height of the cone is equal to twice the radius, so h = 2 * r.
The volume of the cone is given by V = (1/3)π r^2 h.
Substituting the values we found, we have:
V = (1/3)π * [(54/π)^(1/3)]^2 * [2 * (54/π)^(1/3)]
Simplifying this expression, the approximate volume of the cone is:
V ≈ 32.55 m^3
We found that the radius of the sphere is given by r = (54/π)^(1/3).
The height of the cone is equal to twice the radius, so h = 2 * r.
The volume of the cone is given by V = (1/3)π r^2 h.
Substituting the values we found, we have:
V = (1/3)π * [(54/π)^(1/3)]^2 * [2 * (54/π)^(1/3)]
Simplifying this expression, the approximate volume of the cone is:
V ≈ 32.55 m^3