A cylindrical glass of height 25 cm and radius 4 cm has water up to a height of 16 cm. A crow wants to drink water from this glass. The water must be at a height of 20 cm for the crow to reach it. There are some marbles lying around. How many marbles of radius 1 cm should the crow drop into the glass to make the water reach the required height?

Step-by-step solution

Idea: Each sunken marble pushes up water equal to its own volume. The rise needed is a cylinder of water 4 cm tall.

1. Rise needed = 20 − 16 = 4 cm. Volume to be displaced = π × 4² × 4 = 64π cm³.1 mark
2. Volume of one marble = 43π × 1³ = 43π cm³.1 mark
3. Number = 64π ÷ 43π = 64 × 34 = 48 marbles. (The glass is 25 cm tall, so the water does not overflow.)1 mark

Check: 48 marbles × 43π = 64π = π × 16 × 4 ✓.

Answer to write in the exam

Common mistakes that cost marks

• Using the whole height 20 cm (or 16 cm) instead of the rise of 4 cm.
• Using surface area 4πr² for the marble instead of volume.

How this can come in the exam

Try one yourself

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