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Fig. A shows a paper cup in the shape of an inverted right circular cone. Its base radius is 4 cm and its slant height is 8.5 cm.
(a) Find the capacity of the paper cup.
(b) The paper cup is cut along PQ to form the sector in Fig. B. Find (i) the area of the sector, (ii) the angle of the sector.
(a) Height of the cup = [tex]\sqrt{ {8.5}^{2} - {4}^{2} }[/tex] = 7.5 cm The capacity of the cup = [tex] \frac{1}{3} \times \pi \times {4}^{2} \times 7.5[/tex] = 126 cm³ (cor. to 3 sig. fig.)
(b)(i) The area of the sector = [tex]\pi \times 4 \times 8.5[/tex] = 107 cm² (cor. to 3 sig. fig.)
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