Question

Use the image to answer the question.

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)
Responses

There is not enough information to say.
There is not enough information to say.

18 m3
18 m cubed

24 m3
24 m cubed

36 m3

Answer 1

Let the common radius be R. Cone: V = (1/3)πR^2h with h = 2R, so V_cone = (1/3)πR^2(2R) = (2/3)πR^3. Hemisphere: V = (1/2)(4/3)πR^3 = (2/3)πR^3. Thus the hemisphere and cone have equal volumes. Since the cone is 12 m^3, the hemisphere is also 12 m^3, so total = 24 m^3.