Question

Question 7 ( 6 Marks)

Three crayons are held together with an elastic band. The diagram below shows the end of
the crayons and the elastic band. Each of the crayons has diameter of 10 mm. Find the
length of the elastic band in this position.​

Answer 1

Total length of the elastic band in this stretched position = 61.43 mm

Explanation:

The complete Question with the image is attached to this solution

The second image shows the break down of the angle subtended by the elastic band over the crayons at the centre of the circle formed by the crayon's circular shape.

The elastic band extends over 3 of such length of an arc and covers a length of 2 × radius in the spaces between the contact with each crayon. This is also shown in the second attached image.

So, the length of the band will be a sum of 3 diameters and 3 of those arc lengths

Length of an arc is given by

L = (θ/360) × πD

θ = 120°

D = 10 mm

L = (1/3) × 10π = (10π/3) mm

But there are 3 of those, So, total length of the arcs = 3 × (10π/3) = (10π) mm

Length of those 3 diameter regions = 3×10 = 30 mm

Total length of the elastic band in this stretched position = 30 + 10π = 30 + 31.43 = 61.43 mm

Hope this Helps!!!