Theory question 103
Mensuration of Plane Shapes(a) AB is a chord of a circle centre O. If |AB| = 24.2cm and the perimeter of ΔAOB is 52.2cm, calculate ∠AOB correct to the nearest degree.
(b) A rectangular tank 60cm by 80 cm by 100 cm is half filled with water. How many litres of water is it holding?
Show the model answer
Model answer
(a) OA = OB = r: 2r + 24.2 = 52.2, so r = 14 cm.
The perpendicular from O bisects AB: sin(½∠AOB) = 12.1/14 = 0.8643, so ½∠AOB ≈ 59.8° and ∠AOB ≈ 120°.
(b) Volume of water = ½ × 60 × 80 × 100 = 240,000 cm3 = 240 litres.
Explanation
1 litre = 1000 cm³.