(a)
Calculate the area of the shaded segment of the circle shown in the diagram [Take (pi = frac{22}{7})]
(b) A tin has radius 3cm and height 6cm. Find the (i) total surface area of the tin ; (ii) volume, in litres, that will fill the tin to capacity, correct to two decimal places.
Explanation
(a) Area of the shaded segment = Area of sector – Area of triangle
= (frac{theta}{360°} times pi r^{2} – frac{1}{2} ab sin theta)
Area of sector = (frac{63}{360} times frac{22}{7} times 10^{2})
= (55 cm^{2})
Area of triangle = (frac{1}{2} times 10 times 10 times sin 63°)
= (50 times 0.891 = 44.55 cm^{2})
(therefore text{Area of the shaded segment} = 55 – 44.55 = 10.45 cm^{2})
(b) (i) Total surface area = (2pi r (r + h))
= (2 times frac{22}{7} times 3 (3 + 6))
= (frac{132}{7} times 9 = frac{1188}{7})
= (169.71 cm^{2})
(ii) Volume of tin = (pi r^{2} h)
= (frac{22}{7} times 3 times 3 times 6 = frac{1188}{7})
(approxeq 169.71 cm^{3})