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^3 . What is the volume of the whole object?(1 point)
Responses
36 m^3
18 m^3
24 m^3
There is not enough information to say.
To find the volume of the whole object, we need to calculate the volume of the hemisphere and the volume of the cone separately, and then add them together.
The volume of a hemisphere is given by V_hemisphere = (2/3)πr^3, where r is the radius.
The volume of a cone is given by V_cone = (1/3)πr^2h, where r is the radius and h is the height.
Given that the height of the cone is equal to the diameter of the hemisphere, we can say that h = 2r.
Given that the volume of the cone is 12 m^3, we can write:
12 = (1/3)πr^2(2r)
12 = (2/3)πr^3
r^3 = (3/2) * 12/π
r^3 = 9/π
r ≈ 1.704 m (rounded to 3 decimal places since it's a radius)
Now, we can calculate the volume of the hemisphere using the radius we found:
V_hemisphere = (2/3)π(1.704)^3
V_hemisphere ≈ 12.487 m^3 (rounded to 3 decimal places)
Finally, to find the volume of the whole object, we add the volume of the hemisphere (12.487 m^3) and the volume of the cone (12 m^3):
Volume of object = V_hemisphere + V_cone
Volume of object ≈ 12.487 m^3 + 12 m^3
Volume of object ≈ 24.487 m^3
Therefore, the volume of the whole object is approximately 24.487 m^3.
The correct answer is 24 m^3.