Question:
A rectangular sheet of metal measuring 120mm by 75mm has equal squares of side 𝑥 cut from each of the corners. The remaining flaps are then folded up to form an open box. Prove that the volume of the box is given by:
Answer:
Find the maximum volume of the box and the corresponding value of 𝑥.
To determine which value of x will produce the maximum volume, firstly find the second derivative:
Sub in x = 15:
As x = 15 will produce the maximum volume of the box, substitute x = 15 into original equation:
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