Theory question 111
Ratio, Percentages and Rates(a) It takes 8 students two-thirds of an hour to fill 12 tanks with water. How many tanks of water will 4 students fill in one-third of an hour at the same rate?
(b) A chord, 20 cm long, is 12cm from the centre of circle. Calculate, correct to one decimal place, the: (i) angle subtended by the chord at the centre of the circle; (ii) perimeter of minor segment cut off by the chord. [Take π = 3.142]
Show the model answer
Model answer
(a) Half the students for half the time: 12 × ½ × ½ = 3 tanks
(b)(i) Half-angle: tan θ = 10/12 → θ = 39.8°; angle at centre ≈ 79.6°
(ii) Radius = √(10² + 12²) = √244 ≈ 15.62 cm
Arc = 79.61/360 × 2 × 3.142 × 15.62 ≈ 21.7 cm
Perimeter of minor segment ≈ 21.7 + 20 = 41.7 cm
Explanation
The perpendicular from the centre bisects the chord.