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?
A. 18 m^3
B. There is not enough information to say.
C. 36 m^3
D. 24 m^3
C. 36 m^3
To find the volume of the whole object, we first need to find the volume of the hemisphere. Since the height of the cone is equal to the diameter of the hemisphere, the radius of the hemisphere will be half the height of the cone.
Volume of cone = 1/3 * π * r^2 * h
12 = 1/3 * π * r^2 * h
12 = 1/3 * π * (h/2)^2 * h
12 = 1/3 * π * (1/4) * h^3
12 = π/12 * h^3
h^3 = 144/π
h = 3∛(144/π) = 3
Radius of the hemisphere = h/2 = 1.5
Volume of hemisphere = 2/3 * π * r^3
Volume of hemisphere = 2/3 * π * (1.5)^3
Volume of hemisphere = 2/3 * π * 3.375
Volume of hemisphere = 7.08 m^3
Total volume = Volume of hemisphere + Volume of cone
Total volume = 7.08 + 12
Total volume = 19.08 m^3
The correct answer is not listed in the options provided, so it seems that there is not enough information to say.