The diagram shows a circle, centre O, radius r cm. The points A and B lie on circle such that angle AOB = 2θ radians.

i. Find, in terms of r and θ, an expression for the length of the chord AB.

ii. Given that the perimeter of the shaded region is 20 cm, show that r = 10/θ + sin θ.

iii. Given that r and θ can very, find the value of dr/dθ when θ = π/6.

iv. Given that r is increasing at the rate of 15 cm s^-1, find the corresponding rate of change of θ when θ = π/6.

Transcribed Image Text:

B. 20 radrcm