Question

If the height of the cylinder is halved and the diameter is double, by what factor will the volume of the cylinder change

Answer 1

Let the radius be: r and height be h
volume = πr²
if the radius is halved then radius = r/2
and height is doubled, so height= 2h
volume = πr*r/4*2h = π*r²*h/2
Thus the volume will be halved.