The volume of a cone is given by the formula V = (1/3)πr^2h, where r is the radius and h is the height. Since the height of the cone is equal to the diameter of the hemisphere, we know that the height of the cone is equal to 2r.
Given that the volume of the cone is 12 m^3, we can substitute this information into the volume formula and solve for the radius of the cone:
12 = (1/3)πr^2(2r)
12 = (2/3)πr^3
r^3 = 18/π
r ≈ 1.91 m
The volume of a hemisphere is (2/3)πr^3. Since the radius of the hemisphere is equal to the radius of the cone, the volume of the hemisphere is:
V = (2/3)π(1.91)^3 ≈ 7.65 m^3
The total volume of the object is the sum of the volume of the hemisphere and the volume of the cone:
V_total ≈ 12 + 7.65 ≈ 19.65 m^3
Therefore, the volume of the whole object is approximately 19.65 m3.
Use the image to answer the 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 There is not enough information to say. There is not enough information to say. 24 m3 24 m cubed 18 m3
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