Determine the effect of changes in the linear dimensions of a figure on other measures of the figure, such as area.

Example How does this make sense?!
The circumference, in inches, of a certain circle is C, where Absolute value (C minus 20.5) less than or equal to 0.5. Which of the following is a possible area of the circle, in square inches?

Comments

  1. | C-20.5 | <= 0.5
    Using the properties of modulus:
    -0.5 <= C-20.5 OR C-20.5 <= 0.5
    Solving for the above equations,
    Either; C>=20 OR C<=21
    Now, C=Circumference=2*Pi*R where R=Radius of the Circle.
    Thus, 2*Pi*R>=20 OR 2*Pi*R<=21 => R>={20/[2*Pi]} OR R<={21/[2*Pi]}
    Now, We have got two values for "R", the question asks for Area.
    Area={Pi*R*R}, Putting the above values of "R", in the area equation,
    Area is equal to {100/Pi} OR {441/[4*Pi]}.
    The quesion asks for a possible area of the circle, which we have got above, i.e. {100/Pi}.

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