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?
To find the volume of the whole object, we need to add the volume of the cone and the volume of the cylinder.
The formula for the volume of a cone is V = 1/3 * π * r^2 * h, where r is the radius and h is the height.
Since the cone and the cylinder share the same radius and height, we can set the radius and height of both shapes to be the same variable, let's call it r and h.
Therefore, the volume of the cone is V_cone = 1/3 * π * r^2 * h = 50 cm^3.
To find the volume of the cylinder, we can use the formula V_cylinder = π * r^2 * h.
Since the radius and height are the same for the cone and cylinder, we have V_cylinder = π * r^2 * h = π * r^2 * h * 1/3 * 3 = π * r^2 * h/3 = 3 * V_cone.
So, the volume of the whole object is V_whole = V_cylinder + V_cone = V_cone + 3 * V_cone = 4 * V_cone = 4 * 50 cm^3 = 200 cm^3.
Therefore, the volume of the whole object is 200 cm^3.