An engineer wants to know the volume of the following object composed of a hemisphere and a cone. She knows the height of the cone is equal to the diameter of the hemisphere, and the volume of the cone is 12 m3 . What is the volume of the whole object?(1 point)
Responses
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.
Since the height of the cone is equal to the diameter of the hemisphere, we can write h = 2r.
Given that the volume of the cone is 12 m3, we can substitute this information into the volume formula:
12 = 1/3 * π * r^2 * 2r
Simplifying, we get:
12 = 2/3 * π * r^3
r^3 = 18 / π
r = ∛(18 / π)
Now, we need to find the volume of the hemisphere and add it to the volume of the cone.
The volume of a hemisphere is given by the formula V = 2/3 * π * r^3.
Substitute r with the value we found earlier:
V = 2/3 * π * (∛(18 / π))^3
V = 2/3 * π * (18 / π)
V = 12 m3.
Therefore, the volume of the whole object (hemisphere + cone) is 12 m3.