Math, asked by gkdian, 11 days ago

There are two concentric circles such that chord of bigger circle is tangent to the smaller one and the length of the chord is 20 mm. find the area of the ring(shaded region)?

(take π= 22/7m)​

Attachments:

Answers

Answered by mukherjeepragyan0
1

Answer:

The area of the ring or the area of the shaded region is 314.28 mm^{2}

Step-by-step explanation:

Given that, there are two concentric circles where the bigger circle is tangent of the chord and is 20mm.

Now let us consider the outside circle's radius is R, whereas the inner circle's radius is r. The tangent line is perpendicular to the radius of the circle at the point of tangency, hence this triangle is right-angled. In addition, symmetry dictates that the right triangle's side be half the chord length, so I've given it 10mm.

In order to find the area of the shaded region, we need to subtract the area of the big circle from the area of the small circle.

So, The area of the outer circle is πR^{2}

The area of the inner circle is πr^{2}.

Therefore the area of the shaded region is the difference between the two:

 A = π(R^{2} - r^{2})

Since that is a right triangle, Pythagoras theorem is applied, so

    R^{2} = 10^{2} + r^{2}

    R^{2} - r^{2} = 10^{2}

Thus,

   A = π(10^{2}) = π×100

Also π = 22/7

So Area = 314.28mm^{2}                    ( Taking only two decimal values )

Attachments:
Similar questions