A 3D modeler is designing a component of a castle in a video game. She places a cone on top of a cylinder so they line up and share the same radius. The cone and the cylinder share the same height. if the volume of the cone is 50cm^3, what is the volume of the whole object?
___cm^3
To find the volume of the whole object, we need to find the volume of both the cone and the cylinder and add them together.
Given that the volume of the cone is 50cm^3, we can use the formula for the volume of a cone to find the radius:
V = (1/3) * π * r^2 * h
50 = (1/3) * π * r^2 * h
Since the height of the cone and cylinder are the same and the radii are equal, we can equate the volume of the cone to the volume of the cylinder as well:
50 = π * r^2 * h
Now, let's solve these equations to find the values of r and h that satisfy both equations simultaneously:
(1/3) * π * r^2 * h = π * r^2 * h
(1/3) * r^2 = r^2
Subtracting r^2 from both sides of the equation:
(1/3) * r^2 - r^2 = 0
(-2/3) * r^2 = 0
Dividing both sides by -2/3:
r^2 = 0
This means that the radius of the cone is 0, which is not possible. Therefore, it seems there is an error in the information provided as it is not possible to have a cone with a volume of 50cm^3 and a cylinder on top with the same height and radius.