Theory question 108
Mensuration of Plane Shapes(a) Calculate the area of the shaded segment of the circle shown in the diagram. (Take π = 22/7).
(b) A tin has radius 3cm and height 6cm. Find the: (i) total surface area of tin; (ii) volume in litres of liquid that will fill the tin to capacity, correct to two decimal places. (Take π = 22/7).
Show the model answer
Model answer
(a) Sector area = (63/360) × 22/7 × 102 = 55 cm2
Triangle area = ½ × 10 × 10 × sin 63° = 50 × 0.8910 = 44.55 cm2
Segment area = 55 − 44.55 = 10.45 cm2
(b)(i) Closed tin: total surface area = 2πr2 + 2πrh = 2πr(r + h) = 2 × 22/7 × 3 × 9 = 169.71 cm2
(ii) Volume = πr2h = 22/7 × 9 × 6 = 169.71 cm3
1 litre = 1000 cm3, so volume ≈ 0.17 litres
Explanation
Segment = sector minus the triangle formed by the two radii and the chord.