(a) AB is a chord of a circle centre O. If |AB| = 24.2 cm and the perimeter of (Delta) AOB is 52.2 cm, calculate < AOB, correct to the nearest degree.
(b) A rectangular tank 60cm by 80cm by 100cm is half filled with water. How many litres of water is it holding?
Explanation
(a)
(2r + 24.2 = 52.2)
(2r = 52.2 – 24.2 = 28)
(r = 14 cm)
(|AB|^{2} = OA^{2} + OB^{2} – 2(OA)(OB) cos <AOB)
(24.2^{2} = 14^{2} + 14^{2} – 2(14)(14) cos < AOB)
(cos < AOB = frac{14^{2} + 14^{2} – 24.2^{2}}{2(14)(14)})
(cos < AOB = frac{392 – 585.64}{392})
= (frac{-193.64}{392})
(cos < AOB = – 0.4940)
(< AOB = cos^{-1} (0.4940))
= (119.6° approxeq 120°)
(b) Volume of water in the tank = (frac{1}{2} times l times b times h)
= (frac{1}{2} times 60 times 80 times 100)
= (240000 cm^{3})
Number of litres of water = (frac{240000}{1000})
= (240 litres)