Engineering Board Exam Reviewer · Optimization (Maxima and Minima) · hard
A cone-shaped paper cup is to hold 100 cm3 of water. Find the height that minimizes the amount of paper needed to make the cup (i.e., minimizes the lateral surface area).
- 5.76 cm
- 6.20 cm
- 4.98 cm
- 7.05 cm
Answer
A. 5.76 cm
Solution
V= 13π r2h=100 r2=300/π h. The lateral area satisfies S2=π2r2(r2+h2)=90000/h2+300π h. Setting the derivative to 0: -180000/h3+300π=0 h3=600/π h 5.76 cm.
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