A flexible advertising banner is wound around a cylindrical drum

MATHEMATICS · Multi-part · A Level · Mathematics · Trigonometry · Trigonometry

Problem

A flexible advertising banner is wound around a cylindrical drum. When 1.5 m1.5\,\text{m} of the banner has been unwound, it makes an angle of 0.6 rad0.6\,\text{rad} at the centre of the drum. Use this information to answer the questions below. (i) Find the radius of the drum, correct to two decimal places. (ii) Express the central angle of 0.6 rad0.6\,\text{rad} in degrees, giving your answer to the nearest minute. (iii) The banner continues to unwind until the central angle reaches 2π3 rad\dfrac{2\pi}{3}\,\text{rad}. How much additional length of the banner will be unrolled? (Give the answer in centimetres correct to the nearest whole number.)

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