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 50 cm^3, what is the volume of the whole object?
Let's call the height of the cone and the cylinder "h" and the radius "r." Since the cone and the cylinder share the same height and radius, we can use the formulas for the volume of a cone and a cylinder to set up the following equation:
Volume of cone = Volume of cylinder
1/3 * pi * r^2 * h = pi * r^2 * h
Since the radius is the same for both the cone and the cylinder, we can cancel it out:
1/3 * pi * h = pi * h
Now, we can multiply both sides by 3 to solve for the height:
pi * h = 3 * pi * h
h = 3 * h
Since the height of the cone is h, we can conclude that h = 3h, which means h must equal 0. Therefore, the equation is undefined, and we can't determine the volume of the whole object based on the given information.
Please note that there might be a typographical error or missing information in the given problem statement, as it is not possible for the cone and the cylinder to share the same height and radius without further information.