Q38 · Practice questionTechnology-activeComplex familiar5 marks
QUESTION 38 (5 marks)
A 30 cm by 20 cm rectangular sheet has squares of side cm cut from each corner. The sides are folded up to form an open box. Determine the value of that maximises the volume and state the maximum volume to the nearest cubic centimetre.
WORKED SOLUTION
5 marksPractice marking scheme
ANSWER
cm; maximum volume cm.
Worked solution
The volume is , for . Then , giving . Only lies in the domain. It gives cm.
Forms the volume function.
Differentiates the volume function.
Solves the stationary-point equation.
Selects the physically valid value .
Determines the maximum volume, approximately cm.
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