Water height
5.00cm
Pebbles
0
① The Problem
A crow finds water in a bottle with capacity 1 L.
The bottle has base radius 4 cm.
The water is 5 cm deep now.
The crow can only drink when the bottle is full.
Each pebble dropped into the bottle displaces 25 cm3 of water.
How many pebbles are needed?
② Three things to notice
Its capacity (1 L) and its radius (4 cm).
The 5 cm depth. Combined with the radius, this gives the current water volume.
Each pebble displaces 25 cm3 of water — that is, it pushes 25 cm3 of water upward. Pebbles don't create water; they take its place.
③ Predict before you drop
pebbles
Lock in your prediction, then drop pebbles to test it.
④ Test it
⑤ The mathematics
Bottle capacity. 1 L = 1000 mL = 1000 cm3
Water at the start. V = π(4)2(5) = 80π ≈ 251 cm3
Volume still to fill. 1000 - 80π ≈ 749 cm3
Number of pebbles. (1000 − 80π) / 25 ≈ 29.95, so round up to 30.
The crow needs 30 pebbles to fill the bottle. Notice how 1 L and 1000 cm3 describe the same space — one in liquid units, one in cubic units.