This is how it looks like:

enter image description here

It is given that the area of the shaded region is $35 cm^2$.

All of my attempts so far ended up in a two-variable equation in terms of $r_1$ and $r_2$ (the radii of the larger circle and smaller circle respectively).

So, how do I find the area enclosed between the two circles, that is, the area of the larger circle minus the area of the smaller circle?

  • $\begingroup$ No, I mean the area between the smaller circle and larger circle, excluding all other shapes. $\endgroup$ – Wais Kamal Nov 17 '18 at 21:51
  • 1
    $\begingroup$ Then the hint becomes $\frac12(r_1^2-r_2^2) = 35 \implies \pi(r_1^2-r_2^2) = ?$ which is essentially what Manika's answer does. $\endgroup$ – achille hui Nov 17 '18 at 21:53

Say $R_s$ is the radius of small circle and $R_b$ is the radius of big one, then

  1. What you need to find is $S = \pi*(R_{b}^2 - R_{s}^2)$
  2. What you already know is $0.5R_b^2 - 0.5R_s^2 = 0.5(R_b^2 - R_s^2) = 35$ (subtracting the areas of triangles)

From (2) you just find, that $R_b^2 - R_s^2 = 70$ and then substituting it into (1) you get $70\pi$

| cite | improve this answer | |
  • $\begingroup$ Never thought it is that simple, thanks a lot dude :) $\endgroup$ – Wais Kamal Nov 17 '18 at 21:54

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.