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)
○ 36 m³
○ There is not enough information to say.
○ 18 m³
○ 24 m³
The volume of the cone is given as 12 m³. Let V_h be the volume of the hemisphere and V_c be the volume of the cone.
Given that the height of the cone is equal to the diameter of the hemisphere, we can say that the radius of the hemisphere is also equal to the height of the cone.
Volume of a cone: V_c = (1/3)πr²h
Given V_c = 12, we can calculate the radius of the cone (r) by using the formula:
12 = (1/3)πr²h
12 = (1/3)πr²r
36 = πr³
r = ∛(36/π)
r ≈ 2.38 m
Since the radius of the hemisphere is also equal to the height of the cone, we can say that the radius of the hemisphere is 2.38 m.
The volume of a hemisphere is given by: V_h = (2/3)πr³
Substitute r = 2.38 into the formula to find the volume of the hemisphere:
V_h = (2/3)π(2.38)³
V_h = (2/3)π(13.79)
V_h ≈ 29 m³
The volume of the whole object is the sum of the volume of the hemisphere and the volume of the cone:
V_total = V_h + V_c
V_total = 29 + 12
V_total = 41 m³
Therefore, the volume of the whole object is approximately 41 m³. So, the correct option is not given in the choices provided.