Textbook Problem

The surface of a soccer ball is composed of 12 regular pentagons and 20 regular hexagons.

With each side of each regular polygon measuring 4.5 cm, the area of each regular pentagon is 34.9 ${ \mathrm{c}\mathrm{m}}^2$ and area of each regular hexagon is 52.5 ${ \mathrm{c}\mathrm{m}}^2$.

a) What is the surface area of the soccer ball?

b) If the material used to construct the ball costs 0.8 of a cent per square centimeter, what is the cost of the materials used in construction?