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
The volume of a cone is given by the formula Vcone = (1/3)πr^2h, where r is the radius and h is the height.
Since the cone and the cylinder share the same radius and height, the volume of the whole object is given by Vobject = Vcone + Vcylinder.
The volume of the cone is given as 50 cm^3.
To find the volume of the cylinder, we need to find its radius.
Since the cone and cylinder share the same radius, let's call the radius of both the cone and the cylinder as r.
Substituting the known values into the volume formula of the cone, we have:
50 = (1/3)πr^2h
To solve for r, we need another equation that relates r and h.
Since the cone and the cylinder share the same height, let's call the height of both the cone and the cylinder as h.
The volume of the cylinder is given by the formula Vcylinder = πr^2h.
Substituting the known values into the volume formula of the cylinder, we have:
Vcylinder = πr^2h
Since the cone and the cylinder are stacked on top of each other, their volumes add up:
Vobject = 50 + πr^2h
Therefore, the volume of the whole object is 50 + πr^2h cm^3.