a The diagram shows a circle with centre O and radius 42 cm

a) The diagram shows a circle with centre O and radius 42 cm. A and B are points on the circumference such that arc AB an angle of 1109. (Give your answers to 2 decimal places) 110° Calculate the length of arc AB. Use angle in radians. (5 marks) ii) Find the area of the sector AOB (shaded area). (5 marks)

Solution

i ) The radius is 42cm

So, the length of the sector is (angle)/360 *(2*pi*42)

= (110/360)*(2*3.14*42)

= 80.593 cm

ii)

Area of AOB is (110/360)*pi*42^2

= 1692.46 cm^2