Least surface area
Given equal volume and equal height, which solid has the least surface area?
A. A right prism with square base.
B. A right prism with equilateral triangle base.
C. A right circular cylinder.
D. A right prism with regular pentagon base.
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1 solution
Since volume equal base area times high is evident the the circle a regular polygon of infinite sides enclose the maximum area with same perimeter. Pentagon, square and equilateral triangle will follow by this order.