Hello, omkara!

A flexible wire of length 12 metres, is bent into the 3-sided shape.

(Note that the arc PS is not part of the wire.)

The endsegments and are each straight and have equal length m.

while the middle segment forms a circular arc.

The ends of the wire are placed at the edge of a disc of radius 8 m and with centre

The arc forms part of a circle with centre at subtends an angle radians at

The question corncerns the area A within the disc that is enclosed between its edge

and the wire, which is shown shaded.(a) Express the length of the wire PQRS in terms of and .Code:P o 8 *:::* o:::::::: * Q*:::A:::* * *::::::: * x :::::::: o * * * * o * o O 8-L R L S

Hence express in terms of

We have: .

Then: .

(b) Hence show that the area A can be expressed by: .

Substitute [1]: .

. . .

I seriously doubt that angle could be(c) Explain why it is reasonable to choose as the domain for15 radians.

Look at the area function: .

Since , all the factors must be positive.

We have: .

Hence, the domain is: .