The diagram shows a metal plate consisting of a rectangle with sides xcm and rcm and two identical sectors of a circle of radius rcm. The perimeter of the plate is 100 cm.

a. Show that the area, Acm², of the plate is given by A = 50r − r².
b. Express 50r − 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.

Transcribed Image Text:

rcm x cm rcm