A geometry problem

Geometry Level 1

If the 4 circles are congruent, and each have a radius of 3, what is the area of the red region in terms of pi?

36π 36π-9 36-9π 9π

Ross Fasone by Ross Fasone , 21, USA

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.

2 solutions

Consider my diagram on the left.

Area of the red region is equal to the area of the square minus area of the circle. We have

A r e d = 6 2 − π ( 3 2 ) = 36 − 9 π A_{red}=6^2-\pi (3^2)=36-9\pi

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Mihir John
Nov 27, 2014

Joining the centers of the adjacent circles we get a square of side 6 units. The area of the shaded red region is the area of the square - 4 x (1/4 the area of each circle of radius 3) ie. 36- 4 x ( 0.25 x π x 3 x 3) = 36 - 9π

1 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...