Question

While keeping the height of the cone constant, move the vertex of the cone so that it is not directly above the center of the base. Check the Allow

oblique and Freeze height boxes to assist you. Does changing the position of the vertex affect the volume if the height remains the same? Why or
Why not? (Hint: Think of the cone as a stack of disks of decreasing radius.)

Answer 1

ANSWER option 1:

Changing the position of the vertex doesn't change the volume because the height remains the same, all that changes is the position of hypothetical disks. Changing the vertex without changing the height has no effect on the volume of said cone.

ANSWER option 2:

The volume does not change. Cavalieri's principle states that if two three-dimensional figures have the same height and have the same cross-sectional area at every level, then they have the same volume. Cavalieri's principle is applicable to the cone before and after the vertex is changed, assuming that the height is fixed.

Step-by-step explanation: (both answers above are correct)

option 1:

I got that answer correct on edmentum (PLATO)

option 2:

sample answer on edmentum (PLATO)

Answer 2

No, it doesn't.

Explanation:

If we think of the cone as a stack of disks of decreasing radius, and we move the vertex of the cone while keeping the height of the cone, the number of disks don't change nor their radius, it only changes their position respect the original disposition. Then, the volume of the cone remains the same.