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Worksheet: Application of Graphs of Rational Functions

Q1:

Consider the square prism shown in the diagram.

Write its surface-area-to-volume ratio in terms of π‘₯ . Give your answer in standard form.

  • A 2 0 π‘₯ + 2 2 π‘₯ + 6 4 π‘₯ + 8 π‘₯ + 5 π‘₯ + 1 2 3 2
  • B 4 π‘₯ + 8 π‘₯ + 5 π‘₯ + 1 1 6 π‘₯ + 2 0 π‘₯ + 6 3 2 2
  • C 1 2 π‘₯ + 1 8 π‘₯ + 6 4 π‘₯ + 8 π‘₯ + 5 π‘₯ + 1 2 3 2
  • D 1 6 π‘₯ + 2 0 π‘₯ + 6 4 π‘₯ + 8 π‘₯ + 5 π‘₯ + 1 2 3 2
  • E 4 π‘₯ + 8 π‘₯ + 5 π‘₯ + 1 2 0 π‘₯ + 2 2 π‘₯ + 6 3 2 2

The diagram shows the graph of the surface-area-to-volume ratio of the prism as a function of π‘₯ . Which of the following is an approximate value of π‘₯ for which the surface-area-to-volume ratio is 1?

  • A3.3
  • B2.3
  • C1.3
  • D1.5
  • E6