Water height
5.00cm
Pebbles
0
① The Problem
A crow finds water in a bottle with capacity $1\text{ L}$.
The bottle has base radius $4\text{ cm}$.
The water is $5\text{ cm}$ deep now.
The crow can only drink when the bottle is full.
Each pebble dropped into the bottle displaces $25\text{ cm}^3$ of water.
How many pebbles are needed?
② Three things to notice
Its capacity ($1\text{ L}$) and its radius ($4\text{ cm}$).
The 5 cm depth. Combined with the radius, this gives the current water volume.
Each pebble displaces $25\text{ cm}^3$ of water — that is, it pushes $25\text{ cm}^3$ 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. $1\text{ L} = 1000\text{ mL} = 1000\text{ cm}^3$
Water at the start. $V = \pi(4)^2(5) = 80\pi \approx 251\text{ cm}^3$
Volume still to fill. $1000 - 80\pi \approx 749\text{ cm}^3$
Number of pebbles. $\dfrac{749}{25} \approx 29.95$, so round up to $30$.
The crow needs 30 pebbles to fill the bottle. Notice how $1\text{ L}$ and $1000\text{ cm}^3$ describe the same space — one in liquid units, one in cubic units.