(a) It takes 8 students two- thirds of an hour to fill 12 tanks with
(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 12 cm from the centre of the circle. Calculate, correct to one decimal place, the :
(i) angle subtended by the chord at the centre of the circle;
(ii) perimeter of the minor segment cut off by the chord. [Take \(\pi = 3.142\)].
Explanation
(a) \(Time = \frac{2}{3} hour = \frac{2}{3} \times 60 = 40 mins\)
4 students will take \(\frac{8 \times 40}{4} = 80 minutes\)
\(Time = \frac{1}{3} hour = \frac{1}{3} \times 60 = 20 minutes\)
It will take 20 minutes to fill \(\frac{12 \times 20}{80} = 3 tanks\)
(b).jpg)
\(\tan (\frac{\theta}{2}) = \frac{10}{12}\)
\(\frac{\theta}{2} = \tan^{-1} (0.8337) = 39.8°\)
\(\theta = 39.8° \times 2 = 79.6°\)
(ii) Perimeter of minor segment = Length of chord + length of arc
But \(r^{2} = 12^{2} + 10^{2}\)
= \(144 + 100 = 244\)
\(r = \sqrt{244} = 15.62 cm\)
Length of arc = \(\frac{79.6}{360} \times 2 \times 3.142 \times 15.62 = 21.71cm\)
Perimeter of minor segment = 20 + 21.71 = 41.71cm