Use the image to answer the question.
A 3-dimensional cone is placed on top of a 3-dimensional cylinder. One of the cylinder bases is common to the cone, with the same circumference.
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?
(1 point)
To determine the volume of the whole object, we need to calculate the volume of the cylinder and add it to the volume of the cone.
The volume of a cone is given by the formula: Vcone = (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 write:
Vcone = (1/3) * π * r^2 * h
Vcone = 50 cm^3
To find the volume of the cylinder, we use the formula: Vcylinder = 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, we can write:
Vcylinder = π * r^2 * h
The volume of the whole object is the sum of the volumes of the cone and the cylinder:
Vwhole object = Vcone + Vcylinder
Vwhole object = (1/3) * π * r^2 * h + π * r^2 * h
To simplify, we can factor out r^2 * h from both terms:
Vwhole object = (1/3 + 1) * π * r^2 * h
Vwhole object = (4/3) * π * r^2 * h
Since the cone and the cylinder have the same radius and height, we can also write:
Vwhole object = (4/3) * π * r^2 * h = (4/3) * 50 cm^3 = 200/3 cm^3
Therefore, the volume of the whole object is 200/3 cm^3.