Question

A student needs to make a circular cardboard piece with an area between 154 square inches and 616 square inches. The function f(r) relates the area of the cardboard piece, in square inches, to the radius r in inches. Which of the following shows a reasonable domain for f(r)?
7 < r < 14

154 < r < 616

all positive integers less than 7

all positive integers between 14 and 154

Answer 1

The area of the circle by definition is given by:
 $f (r) = \pi * r ^ 2$
 For f (r) = 154:
 $154 = \pi * r ^ 2$
 Clearing r we have:
 $r ^ 2 = 154 / 3.14 r = \sqrt{154/3.14} r = 7$
 For f (r) = 616:
 $616 = \pi * r ^ 2$
 Clearing r we have:
 $r ^ 2 = 616 / 3.14 r = \sqrt{616/3.14} r = 14$
 Answer:
 a reasonable domain for f (r) is:
 7 <r <14