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
36 m3
36 m cubed
24 m3
24 m cubed
There is not enough information to say.
There is not enough information to say.
18 m3
The correct answer is 36 m3.
To find the volume of the whole object, we need to first find the volume of the hemisphere and then add it to the volume of the cone.
The volume of a hemisphere is given by the formula V = (2/3)πr^3, where r is the radius of the hemisphere. Since the height of the cone is equal to the diameter of the hemisphere, we can say that r = h/2.
Given that the volume of the cone is 12 m3, we can use the formula for the volume of a cone, V = (1/3)πr^2h, to find the value of r.
12 = (1/3)πr^2h
12 = (1/3)π(r^2)(2r)
12 = (2/3)πr^3
r^3 = (3/2) * 12/π
r^3 = 18/π
r ≈ 1.92
Now, we can find the volume of the hemisphere using V = (2/3)πr^3:
V = (2/3)π(1.92)^3
V ≈ 23.95 m3
Therefore, the volume of the whole object (hemisphere + cone) is approximately 23.95 + 12 = 35.95 m3, which can be rounded to 36 m3.