Volume of Cones, Cylinders, and Spheres Quick Check
4 of 54 of 5 Items
Question
Use the image to answer the question.
A cone is placed inside a cylinder. The apex of the cone touching the center of the top circle of the cylinder is highlighted with a dot. The cone with its base is drawn in dashed lines. The base of the cone is common with the base of the cylinder.
A sculptor created a design by carving a cone out of a cylinder. The cone and cylinder share the same radius and height. If the volume of the cylinder before removing the cone is 54 in.3 , what is the volume of the amount remaining?(1 point)
Responses
18 in.3
18 in. cubed
36 in.3
36 in. cubed
40 in.3
40 in. cubed
27 in.3
To find the volume of the amount remaining after carving out the cone, you need to subtract the volume of the cone from the volume of the cylinder.
The volume of a cylinder is given by the formula:
Volume = πr^2h
Since the cone and cylinder share the same radius and height, the volume of the cylinder is equal to the volume of the cone.
So, the volume of the cone is also given by the formula:
Volume = (1/3)πr^2h
Since the volume of the cylinder before removing the cone is 54 in^3, this means the volume of the cone is also 54 in^3.
To find the remaining volume, we subtract the volume of the cone from the volume of the cylinder:
Remaining Volume = 54 in^3 - 54 in^3 = 0 in^3
Therefore, the volume of the amount remaining is 0 in^3. None of the options provided (18 in.3, 36 in.3, 40 in.3, 27 in.3) are correct.