Question

the area of the shaded region between two concentric circles is 286 cm2. If the diffrence of the radii of the two circles is 7 cm find the sum of their radii

Answer 1

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Answer 2

Answer:

13 cm

Step-by-step explanation:

Refer the attached figure

Let the inner radius be r

let outer radius be R

We are given that difference of the radii of the two circles is 7 cm  i.e. R-r = 7cm

Area of inner circle = $\pi r^{2}$

Area of outer circle =  $\pi R^{2}$

So, area of shaded region= $\pi R^{2}-\pi r^{2}$

⇒$286=\pi (R^{2}- r^{2})$

⇒$286 = \pi (R-r)(R+r)$

⇒$286 = \frac{22}{7}(7)(R+r)$

⇒$\frac{286}{22} = (R+r)$

⇒$13= (R+r)$

Thus the sum of their radii is 13 cm