How deep was the water?
A hard-level "Length" problem.Every tilting problem rests on one fact: the volume does not change. Work out whether the shape is a triangular prism or a trapezoidal one, then swap it for an equal volume.
GivenA tank 20 cm long, 10 cm deep, 15 cm high. Tilted, the surface reaches 12 cm up the right wall
Hints
- The one thing to hold on to: tilting the tank spills nothing and adds nothing. Only the shape has changed; the amount is the same.
- Seen from the side, the water is now a right triangle: base 20 cm, height 12 cm.
- The water is a triangular prism. The side triangle is 20 × 12 ÷ 2 = 120 cm², and the tank is 10 cm deep, so the water is 1200 cm³.
- Redraw with the tank level again. Now the water is a cuboid: its base is 20 × 10, and it holds the same amount of water.
- Depth is "volume ÷ base area": 1200 ÷ (20 × 10)
Answer 6cm
More "Length" problems
- a + b + c = ?
- What is the side of the square?
- How long is MN?
- How long is the rope?
- How long is the pole's shadow?
- How far does the centre travel?