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 m'. What is the volume of the whole object?
(1 point)
To find the volume of the entire object, we first need to find the volume of the hemisphere and then the volume of the cone.
1. Volume of the cone:
V_cone = (1/3)πr^2h
Given that the volume of the cone is 12 m^3 and the height of the cone is equal to the diameter of the hemisphere, which means the height of the cone is equal to the radius of the hemisphere. Let's say the radius is r. Therefore, h = r.
12 = (1/3)πr^3
36 = πr^3
r^3 = 36/π
r ≈ 3.3855 m
2. Volume of the hemisphere:
The volume of a hemisphere is (2/3)πr^3.
Given that the radius of the hemisphere is equal to the height of the cone, which is equal to r ≈ 3.3855 m.
V_hemisphere = (2/3)π(3.3855)^3 ≈ 72.7652 m^3
3. Volume of the entire object:
V_object = V_cone + V_hemisphere
V_object = 12 + 72.7652
V_object ≈ 84.7652 m^3
Therefore, the volume of the whole object is approximately 84.7652 m^3.