Compute the required ratio

Geometry Level pending

Circles of equal radii are inside a rectangle as shown. What is the ratio of the shaded area to the unshaded area?

15 ( 4 − π ) 5 π \dfrac{15(4-\pi)}{5\pi} 60 − 15 π π \dfrac{60-15\pi}{\pi} 4 − π π \dfrac{4-\pi}{\pi} π 4 + π \dfrac{\pi}{4+\pi}

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

Consider my diagram. Let the radius of one circle be 1 1 , then the diameter is 2 2 .

a r e a o f r e c t a n g l e = 10 ( 6 ) = 60 area~of~rectangle=10(6)=60

u n s h a d e d a r e a = 15 ( π ) ( 1 2 ) = 15 π unshaded~area=15(\pi)(1^2)=15\pi

s h a d e d a r e a = 60 − 15 π shaded~area=60-15\pi

Therefore, the desired ratio is

r a t i o = 60 − 15 π π = 15 ( 4 − π ) 15 π = 4 − π π ratio=\dfrac{60-15\pi}{\pi}=\dfrac{15(4-\pi)}{15\pi}=\boxed{\dfrac{4-\pi}{\pi}}

0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...