A student measures the circumference of a circular pipe. He wraps a length of string around the pipe five times and marks it with ink, as shown in the photograph.

(a) The student unwraps the string and holds it against a ruler with a centimeter scale. The next photograph shows the first two ink marks on the string.

(i) Estimate the circumference of the pipe, using the photograph of the string and the centimeter scale. Give your answer to two significant figures.

→ Because the student left marks for every wrap around the pipe, the distance between the two marks is approximately the circumference of the pipe.

→ 47.3 - 41.9 = 5.4 cm

(ii) The student finds that the total length of string for 5 turns is 25.6 cm. Calculate the average (mean) circumference of the pipe using this value.

→ 5 turns means 5 circumferences.

→ average circumference = 25.6 / 5 = 5.12 cm

(iii) The student measures the diameter of the pipe using a digital caliper.

The caliper shows that the diameter is 15.10 mm. Calculate the circumference of the pipe using the formula circumference = diameter × π

→ circumference = 15.10 x π = 47.44 mm = 4.744 cm

(b) The student uses two methods to find the circumference

- averaging, using a measured length of string
- calculating, using the digital caliper reading

Explain why the two methods are likely to give different results.

Possible answers:

- The equation to calculate the circumference of the pipe is valid only for circles; the pipe may not be perfectly circular.

- The width of the pen mark may affect the readings.

- There may be parallax error when using the ruler; the readings may be different when viewed from different angles.

- The caliper may not be properly calibrated and give results with errors.

- Caliper and ruler have different precision.

- The caliper may not have been placed at right angles.

- The thickness of the string will make the diameter bigger.

- The string may have stretched during the experiment.