Question

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

Answer 1

So is there enough informaion in the question i asked yes or no?

Answer 2

To find the volume of the whole object, we need to know the radius of the hemisphere. Since the height of the cone is equal to the diameter of the hemisphere, the radius of the hemisphere is half the height of the cone.

Let's substitute the given information into the formula for the volume of a cone: V = (1/3)πr^2h, where V is the volume, r is the radius, and h is the height.

Given that the volume of the cone is 12 m^3, let's use the formula to solve for r:

12 = (1/3)πr^2h
12 = (1/3)πr^2(d)
12 = (1/3)πr^2(2r)
12 = (2/3)πr^3
6 = (2/3)πr^3
18/π = r^3
r ≈ 2.676

Now we can find the volume of the hemisphere: V_hemi = (2/3)πr^3

V_hemi = (2/3)π(2.676)^3
V_hemi ≈ 36.02 m^3

Finally, to find the volume of the whole object, we sum the volume of the hemisphere and the volume of the cone: V_object = V_hemi + V_cone = 36.02 + 12 = 48.02 m^3

Therefore, the volume of the whole object is approximately 48.02 m^3.

Answer 3

No, there is not enough information in the given question to determine the volume of the whole object.