Related Rates · Constant-Rate Fill

The graph is the shape of the flask

Five flasks, same liquid pouring in at the same rate. Because dh/dt = k / A(h), the water climbs fast where the glass is narrow and crawls where it's wide — so each height-vs-time curve is a fingerprint of its geometry. Drag the scrubber to fill them and draw the graphs yourself.

Time

t = 0.00 s

Reveal full curves

Predict first: before you touch the scrubber, sketch the height-vs-time graph you expect for each flask. Then fill them and see how close you were — and where a curve bends differently than you thought, look back at the glass and ask what the width is doing there.

Random flask: tap New shape for a wobbly mystery. Can you read its silhouette off the curve before you scrub?