A semicircular piece of wood is 20 cm thick Let b denote the

A semicircular piece of wood is 20 cm thick. Let b denote the length of the base in cm. Write an equation for a function S that relates the length of the base to the surface area of the wood.

A) S(b) = 20b + b

B) S(b) = b + (b/2) + (b/2)²

C) None of the above

D) S(b) = 20b + 20 (b/2) + (b/2)²

E) S(b) = 20b + 20b + 2b

Solution

surface area of top,bottom =(1/2)(b/2)² each, surface area of circular side=20*(b/2),surface area of flat side=20b

surface area =(1/2)(b/2)²+(1/2)(b/2)²+20*b +20*(b/2)

surface area =(b/2)²+20b +20(b/2)

surface area =20b  +20(b/2) + (b/2)²

S(b) = 20b + 20(b/2) + (b/2)²