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 24 m3 24 m cubed 36 m3 36 m cubed There is not enough information to say. There is not enough information to say. 18 m3
The volume of a cone is given by V = (1/3)πr^2h, where r is the radius and h is the height. Given that the height and diameter are equal for the cone, we can say that the radius of the cone is half the height.
Therefore, the volume of the cone can be written as 12 = (1/3)π(h/2)^2h.
Solving for h, we get h = 4. Therefore, the height of the cone is 4 meters, and the diameter of the hemisphere will also be 4 meters.
The volume of a hemisphere is V = (2/3)πr^3. Substituting the diameter of 4 meters, we get V = (2/3)π(2)^3 = (16/3)π.
Adding the volume of the cone and the hemisphere, we get:
V_total = V_cone + V_hemisphere
V_total = 12 + (16/3)π
V_total ≈ 36 m^3
Therefore, the volume of the whole object is 36 m^3.