How long is the rope?
A hard-level "Length" problem.Three logs or four, the curved part of a rope going once round is always one full circle. It is "the straight parts + one circumference", every time.
GivenThree logs of radius 5 cm tied once around with a taut rope / π = 3.14
Hints
- Split the rope into straight parts and curved parts. Start with the three straight parts.
- Each straight part is as long as the line joining the two centres (dotted). That gap is two radii: 5 × 2 = 10 cm, and there are three: 30 cm.
- What is left are the three arcs wrapped round the logs. Each one turns through 120°.
- Three lots of 120° make 360° — the three arcs together are exactly one whole circle. No need to work them out one by one.
- That circle's circumference is "2 × radius × π" = 2 × 5 × 3.14 = 31.4 cm.
- Add the 30 cm of straight rope to the 31.4 cm of curve: 30 + 31.4
Answer 61.4cm
More "Length" problems
- a + b + c = ?
- What is the side of the square?
- How long is MN?
- How long is the pole's shadow?
- How deep was the water?
- How far does the centre travel?