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

7 < r < 14

Explanation:

Answer 2

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 = √(154/3.14) r = 7`
For f (r) = 616:

`616 = \pi * r ^ 2`
Clearing r we have:

`r ^ 2 = 616 / 3.14 r = √(616/3.14) r = 14`
Answer:
a reasonable domain for f (r) is:
7 <r <14