Circle area ratio

Geometry Level 3

The diagram above shows a rectangle ABCD with length l l and breadth b b .
A pink semicircle is inscribed inside this rectangle.
And a green circle is inscribed inside the region between the semicircle and the rectangle as shown.
Find

area of the semicircle area of the circle . \dfrac{\text{area of the semicircle}}{\text{area of the circle}} .

Image Credit : Theroy vs Theories (facebook).
(2π(π-l))/l^2 4π/(4- π) None of the these 4π/l

Sunny Dhondkar by Sunny Dhondkar , 20, India

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2 solutions

Sunny Dhondkar
Aug 31, 2016

Refer this solution in the image, with high accuracy

0 Helpful 0 Interesting 0 Brilliant 0 Confused

The ratio between the area of the semi circle and small circle is (pi/2)/pi(3-2sqrt2)^2 or approximately 16.985...

0 Helpful 0 Interesting 0 Brilliant 0 Confused

how did you get that?

Sunny Dhondkar - 4 years, 9 months ago

The length has to be exactly twice the breadth.

A Former Brilliant Member - 4 years, 9 months ago

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