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

@Godlovesme

Answer 1

the area depends on the radius right

Answer 2

yes

Answer 3

so the dependent will be the area --> f(r) --> range
independent will be radius --> r --> domain

Answer 4

confused?

Answer 5

yes, kind of.

Answer 6

I was thinking the answer would be A, but I'm not positive

Answer 7

First define the area of a circle:\[A=\pi r^2\]

Answer 8

How you're given \(A_1 = 616~,~ A_2 = 154\)

Answer 9

Now*.

Answer 10

To get your radius.

\[\sqrt{\frac{ A }{ \pi }} \]

Answer 11

So to find the radius of each, as @dtan5457 mentioned, \[r^2 = \frac{A}{\pi} \implies r = \sqrt{\frac{A}{\pi}}\]

Answer 12

Now find \(r_1~,~r_2\) with respect to \(A_1~,~A_2\)

Answer 13

\[A=\pi r^2\]

This is the regular formula for area of a circle, so that's why you would use the first formula as a vice versa to get back to your original radius.

Answer 14

\[r_1 = \sqrt{\frac{A_1}{\pi}} = \sqrt{\frac{616}{\pi}}\]\[r_2 = \sqrt{\frac{A_2}{\pi}} = \sqrt{\frac{154}{\pi}}\]

Answer 15

Your two areas were originally 154 square inches and 616 square inches.

Put a square root on your calculator, and divide those numbers by the pi key.

Answer 16

@Jhannybean

already did the hard part for you