A circle taken for a walk
Meet properly — the Greek letter pi, said pie, worth about 3.14159. It's the circle's own number: every circle's distance around is π times its distance across, no exceptions, ever. A cylinder is a circle taken for a walk, so its volume stacks the circle floor up the height: — read aloud: V equals pi r squared h, with the radius of the circle floor, the height it stands, and the volume it holds.
Two habits keep cylinders honest. First, the square touches ONLY the radius — means π × r × r. Second, make sure you're actually holding the radius: problems love to hand you the diameter, the full width, and the radius is half of it. Feed the formula a diameter and the answer comes out four times too proud — the square doubles the damage.
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