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.
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)
1 answer