(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)
(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