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)

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Answer 1

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.