Two sectors have the same central angle of but belong to circles of radii and respectively

MATHEMATICS · Subjective · A Level · Mathematics · Trigonometry · Trigonometry

Problem

Two sectors have the same central angle of 60∘60^{\circ} but belong to circles of radii 5 cm5\,\mathrm{cm} and 8 cm8\,\mathrm{cm} respectively. (i) Without using any formula for sector area, explain which sector has the longer arc and why. (ii) Justify, using the idea of proportion, which sector has the larger area. (iii) Calculate the difference between the areas of the two sectors.

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