ratio of areas of two circles

Geometry Level 2

A square is inscribed in a circle and a circle is inscribed in this square as shown. What is the ratio of the area of the big circle to the area of the small circle?

4 : 3 4:3 2 : 0.5 2:0.5 2 : 1 2:1 3 : 1 3:1

A Former Brilliant Member by A Former Brilliant Member

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Let the side length of the square be 10 10 . Consider my diagram. The ratio of their areas is

r a t i o = a r e a o f b i g c i r c l e a r e a o f s m a l l c i r c l e = π 4 ( 10 2 ) 2 π 4 ( 10 ) 2 = 100 ( 2 ) 100 = 2 1 \large{\color{#69047E}ratio=\dfrac{area~of~big~circle}{area~of~small~circle}=\dfrac{\dfrac{\pi}{4}(10\sqrt{2})^2}{\dfrac{\pi}{4}(10)^2}=\dfrac{100(2)}{100}=\color{#D61F06}\boxed{\dfrac{2}{1}}}

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Nice solution

Ramiel To-ong - 2 years, 4 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...