Celebrity chef Pepper Bee has opened a new restaurant and is charging diners £630 for a piece of his signature ‘Croesus’ cake. The chef claims that the price reflects the high cost of the gold foil that is placed on top of each slice of cake, but a suspicious and disgruntled customer has decided to investigate this claim.
The shaded area in the diagram below shows the shape of the piece of gold foil that is placed on top of each slice of cake:
The shape is that of a rectangle, from which four identical curved sections have been removed. The rectangle is bounded by the positive - and -axes and the lines and . The shape of one of the curved sections in the diagram can be described by the curve with equation
All units are given in centimetres.
Given that gold foil costs per , work out the cost of the gold foil on a piece of Pepper Bee’s Croesus cake. Give your answer to 2 decimal places.