Q1.
Anish and his parents fixed electric string lights on the arches of the verandah of their house, as shown in Fig. 5.7, for a celebration at home. How would they have measured the required length of string lights?
Answer
The arches are curved, so a stiff metre scale is of no use. They would have measured the curve with a thread (or with a flexible measuring tape), and then straightened the thread along a metre scale.
The thread method, step by step:
- Tie a knot at one end of the thread and hold it at the starting point of the first arch.
- Press the thread along the arch with your fingers so that it follows the curve exactly, without stretching it and without leaving it slack (Fig. 5.8).
- Mark the thread with a pen at the point where the arch ends.
- Straighten the thread on a table and measure the marked portion with a metre scale.
- Repeat for each arch and add up the lengths.
A worked example. Suppose the verandah has 3 arches and the thread for one arch measures 2 m 40 cm:
Length of one arch = 2 m 40 cm = 2.40 m
Number of arches = 3
Total = 3 × 2.40 m = 7.20 m
In centimetres: 7.20 m × 100 cm/m = 720 cm
Adding about 10% extra for the drooping and for joining = 7.20 m + 0.72 m ≈ 8 m of string lights
Number of arches = 3
Total = 3 × 2.40 m = 7.20 m
In centimetres: 7.20 m × 100 cm/m = 720 cm
Adding about 10% extra for the drooping and for joining = 7.20 m + 0.72 m ≈ 8 m of string lights
Why the thread works: the thread takes the shape of the curve, so the length of thread used is the length of the curve. Straightening it does not change how much thread there is — it only turns a curved length into a straight one that a scale can read.
Tip: Use a thread that does not stretch — cotton or jute, not elastic or nylon fishing line. If the thread stretches while you press it along the arch, your answer will be too large and you will buy more lights than you need.