CASE STUDY CHALLENGE

AOD: Optimizing the Golden Box

A man has an expensive square-shaped piece of golden board of side 36 cm. He wants to turn it into a box without a top by cutting a square from each corner and folding up the flaps.

Open Box Cutting Diagram

Let \( x \) cm be the side of the square which is cut from each corner.

Answer the following questions:

(i) Find the expression for the volume (\( V \)) of the open box in terms of \( x \). [1]
(ii) Find the derivative \( \frac{dV}{dx} \). [1]
(iii)

(a) Find the value of \( x \) for which the volume (\( V \)) is maximum.

— OR —

(b) Find the maximum volume of the open box.

 [2]
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