Engineering Board Exam Reviewer · Optimization (Maxima and Minima) · medium
A rectangle with a perimeter of 80 cm is rotated about one of its sides to form a cylinder. What radius (the side perpendicular to the axis) gives the maximum volume?
- 20 cm
- 13.33 cm
- 26.67 cm
- 30 cm
Answer
C. 26.67 cm
Solution
Let the radius be r, so the height is h=40-r. V=π r2(40-r) and V'=π(80r-3r2)=0 r=80/3 26.67 cm.
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