Question

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A hemisphere is placed on top of an inverted cone. The back of the circumference, the radius, and the perpendicular height of the cone are marked with dashed lines. The radius and the height make a right angle and are perpendicular.

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)

There is not enough information to say.

24 m3


18 m3


36 m3

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Answer 1

Let the hemisphere radius be r. Then the cone height h = diameter = 2r.

Cone volume = (1/3)πr^2h = (1/3)πr^2(2r) = (2/3)πr^3.

Hemisphere volume = (1/2)(4/3)πr^3 = (2/3)πr^3.

So the hemisphere and cone have equal volumes. Since the cone's volume is 12 m^3, the hemisphere is also 12 m^3, so the total = 12 + 12 = 24 m^3.