To find the volume of the whole object, we need to find the volume of the cylinder and then 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 of the cone and h is the height of the cone.
Since the cone and the cylinder share the same radius and height, the volume of the cylinder will be:
Vcylinder = π * r^2 * h
Given that the volume of the cone is 50 cm^3, we have:
50 = (1/3) * π * r^2 * h
We also know that the volume of the whole object is the sum of the volumes of the cone and the cylinder:
Vwhole = Vcone + Vcylinder
To find the volume of the whole object, we need to find the value of Vcylinder.
From the equation 50 = (1/3) * π * r^2 * h, we can rearrange it to solve for r^2:
r^2 = (50 * 3) / (π * h)
Substituting this value of r^2 into the equation for Vcylinder, we get:
Vcylinder = π * ((50 * 3) / (π * h)) * h
Simplifying, we have:
Vcylinder = 150 cm^3
Now we can find the volume of the whole object:
Vwhole = Vcone + Vcylinder
Vwhole = 50 cm^3 + 150 cm^3
Vwhole = 200 cm^3
Therefore, the volume of the whole object is 200 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 answer
1 answer