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 cm3 , what is the volume of the whole object
To find the volume of the whole object, we need to find the volume of the cylinder and add it to the volume of the cone.
The volume of a cone is given by the formula V = (1/3) * π * r^2 * h, where r is the radius and h is the height.
Given that the volume of the cone is 50 cm^3, we can substitute V = 50 cm^3 into the formula and solve for the radius squared (r^2). Let's call the radius of the cone (and the cylinder) r.
50 cm^3 = (1/3) * π * r^2 * h
Simplifying the equation, we have:
150 cm^3 = π * r^2 * h
Since the height of the cone and cylinder are the same, we can ignore the height, which means r^2 = 150 cm^3 / π.
Now, the volume of a cylinder is given by the formula V = π * r^2 * h, where r is the radius and h is the height.
Since the cylinder and the cone share the same radius and height, the volume of the cylinder is the same as the volume of the cone.
Therefore, the volume of the whole object is:
Volume = Volume of cone + Volume of cylinder
= 50 cm^3 + 50 cm^3
= 100 cm^3
So, the volume of the whole object is 100 cm^3.