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

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

anonymous · Answer

So area of a circle is determined using the equation A=pi*r^2
Your area range is between 154 and 616, so we can say that 
154<pi*r^2<616

Now we can treat this system just like any other equation and divide out the pi to isolate the radius term...

154/pi < r^2 < 616/pi

and take the square root:

sqrt(154/pi) < r < sqrt(616/pi)

plugging this into a calculator reaaally quick gives you 

7.00... < 14.00...

you just want approximate values so that you can just round off and get a range of 7 to 14in

anonymous · Answer

is it a because of the numbers after square root? 
@LifeEngineer

anonymous · Answer

sorry, I don't quite understand your question?

anonymous · Answer

lol after you got 7 and 14 from the square root wouldn't that make it 
7<r<14 and that is A

anonymous · Answer

@LifeEngineer

anonymous · Answer

okay i was right

anonymous · Answer

yes