A sector of a circle, radius r cm, has a perimeter of 60 cm a Show that the area, Acm 2 , of the sector is given by A 30r r 2 b Express 30r r 2 in the form a (r b) 2 , where a and b are constants Given that r can vary c find the value of r at which A is a maximum d find this stationary value of A ...

a The perimeter of the sector is the sum of the arc length and the two radii which is given ...

A sector of a circle, radius r cm, has a perimeter of 60 cm. a. Show that

Question:

A sector of a circle, radius r cm, has a perimeter of 60 cm.
a. Show that the area, Acm², of the sector is given by A = 30r − r².
b. Express 30r − r² in the form a − (r − b)², where a and b are constants.
Given that r can vary:
c. find the value of r at which A is a maximum
d. find this stationary value of A.