Question

Does the volume of a cone stay the same if you add 1 unit to the radius and subtract 1 unit from the height

Answer 1

To answer the question we proceed as follows:
suppose a cone has a height x units and radius x units
volume will be:
v=1/3πr²h
V=1/3πx³ cubic units


when we add 1 unit to the radius and subtract 1 unit from the height the volume will be:
v=1/3π(x+1)²(x-1)
v=1/3π(x³+x²-x-1) cubic units

comparing the above values for volume we conclude that the volume will not be the same. This means the volume won't stay the same after changes.