Theory question 113
Mensuration of Plane Shapes(a) In the daigram, the radius of the sector of circle centre O, is 7 cm and ∠MON is 60°. Find, correct to one decimal place, the area of the shaded portion. [Take π = 22/7]
(b) The x and y intercepts of a straight line are −3/4 and 2/7 respectively. Find the equation of the line.
Show the model answer
Model answer
(a) Area of sector OMN = 60/360 × 22/7 × 7 × 7 = 77/3 ≈ 25.67 cm²
OT = 7 cos 60° = 3.5 cm, NT = 7 sin 60° ≈ 6.062 cm; area of triangle ONT = ½ × 3.5 × 6.062 ≈ 10.61 cm²
Shaded area = 25.67 − 10.61 ≈ 15.1 cm²
(b) The line passes through (−3/4, 0) and (0, 2/7); gradient = (2/7)/(3/4) = 8/21
y = (8/21)x + 2/7, i.e. 21y = 8x + 6
Explanation
The shaded part is the sector minus the right-angled triangle ONT.