Question

The area of circle B is 36 times greater than the area of circle A. The radius of circle B is 30. What is the radius of circle A?

Answer 1

Please provide an explanation with your answer.

Answer 2

Let A denote the area.
\( \Large A_B=36A_A\)
\( \Large A_B=\pi r_B^2 = \pi (30)^2\)
So
\(\Large \pi (30)^2 = 36 A_A = 36 (\pi r_A^2)\)

Answer 3

then you just need to solve for \(\Large r_A\)

Answer 4

@kirbykirby I can kinda see where this is going.. but it looks a but confusing. Can you explain it further? Like the step by step process?

Answer 5

*a bit

Answer 6

Ok.
So I am denoting \(\Large A_A\) to be the area of circle A, and \(\Large A_B\) to be the area of circle B.

Now the problem says that circle B's area is 36 times larger than than of A's, which is why I set up the first equation as:
\(\Large A_B = 36 A_A\)

Answer 7

Okay, I understand that part. @kirbykirby

Answer 8

Ok so now you know that the formula for the area of a circle to be \(\Large \pi r^2\)
Since both circle A and B have different lengths for their radius, I will denote the radius of A with with a subscript, i.e. \(\Large r_A\), and the radius for B to be \(\Large r_B\)

Answer 9

Okay. @kirbykirby

Answer 10

Ok so that's why the area of circle A becomes \(\large A_A = \pi r_A^2\)
And the area for circle B becomes \(\large A_B = \pi r_B^2\).

Going back to the original equation I wrote:, we can substitute those formulas:
\(\large \color{blue}{A_B}=36\color{red}{ A_A}\)

\(\large \color{blue}{\pi r^2_B}=36\color{red}{ \pi r_A^2} \)

Answer 11

Alright, I think I understand it now. @kirbykirby

Answer 12

great :) all you have to do is substitute 30 for \(\large r_B\) and then solve for \(\large r_A\) :)

Answer 13

The answer is 5? @kirbykirby

Answer 14

yes! :)

Answer 15

Thank you so much! I can't even express how thankful I am for your help. ^^ One other question, would the same format of what you just did apply to this equation? "The area of circle B is 25 times greater than the area of circle A. The radius of circle A is 3. What is the radius of circle B?" @kirbykirby

Answer 16

Your welcome :)

Yes it is really the same type of question. Instead of 36, the number is 25 here. Also, here they give you the radius for A rather than for B.

Answer 17

Okay so I'd just set up the equation the exact same way and just substitute different numbers?

Answer 18

@kirbykirby

Answer 19

yes

Answer 20

\[A _{B}=25A _{A}\]
\[A _{B}=\pi r _{B}^{2}=\pi r^2\]
So like this? Where would the area of A come in? @kirbykirby

Answer 21

\(A_A = \pi r_A^2\)
And they give you the value \(r_A= 3\) in the problem.

Answer 22

Okay so, \[25\pi3_{A}^{2} = \pi r _{B}^{2}\] The radius is 15? @kirbykirby