Question

An archery target consists of a circular bull's-eye with radius x, surrounded by four rings with width y. What is the area of the outermost ring in terms of x and y?

Answer 1

given:
bull's eye radius= x
width of surrounding rings=y

solution:
Radius of the circle=x+4y
Area of the outermost ring=Area of the circle-Area of the penultimate ring =Ď€(x+4y)^2-Ď€(x+3y)^2
=Ď€(x^2+8xy+16y^2-x^2-9y^2-6xy)
=Ď€(2xy+7y^2)
hence the area of the outermost ring in terms of x and y is π(2xy+7y^2).