Q165 · Practice questionTechnology-freeComplex unfamiliar6 marks
QUESTION 165 (6 marks)
An open-top box with a square base has volume . Let the base side length be cm and the height be cm, as shown. Determine the dimensions that minimise the amount of material required to make the box.
WORKED SOLUTION
6 marksPractice marking scheme
ANSWER
cm and cm.
Worked solution
The volume condition is , so . The material area is . Thus . Setting gives , so . Then . Also , confirming a minimum.
Uses the volume constraint to express in terms of .
Forms the material-area function.
Differentiates the area function.
Solves the stationary-point equation.
Determines the height.
Justifies that the dimensions give a minimum.
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