How does the volume of a cylinder change when its diameter is halved? explain .

The answer is: it will decrease 4 times.

Let d be diameter and h height of a cylinder

The volume of a cylinder is:
V1 = π * (d/2)² * h = π * d²/4 * h = π * d² * h / 4
If diameter is halved, the volume is:
V2 = π * ((d/2)/2)² * h = π * (d/4)² * h = π * d²/16 * h = π * d² * h / 16

Now, let's compare them:
V1 / V2 = (π * d² * h / 4) / (π * d² * h / 16)

π * d² * h can be cancelled out:
V1 / V2 = (1/4) / (1/16) = (1/4) * 16 = 16/4 = 4

Therefore, the volume of the smaller cylinder will decrease 4 times.