A six meter long string is cut into two pieces. The first piece, of length , is used to make a circle; the second, of length , to make a square. What value of minimizes the sum of the areas of the circle and the square? ( is allowed to be 0 or 6.)
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A six meter long string is cut into two pieces. The first piece, of length x, is used to make a circle; the second, of length 6-x, to make a square. What value of x minimizes the sum of the areas of the circle and the square? (x is allowed to be 0 or 6.) (A) x=24π/(1+4π). (B) x=6π/(4+π). (C) x=6. (D) x=1/2π.
Single-variable optimisation has come up 37 times in 6 exams since 2010.
This question is on Applied optimisation, part of Single-variable optimisation in Mathematics.
Maximising profit, revenue or area and minimising cost or time in applied settings.
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Question from the DSE 2013 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.