Area QUESTION! (circles within circles)

Mar 2013
142
0
Vancouver
Hi so my question is how do i find the area of the smaller circles if i don't have the radius of the smaller circles but only the large one? here is the question context

"The cross section of a large circular conduit with radius 12.00 cm has seven smaller equal circular conduits within it."

a) calculate the shaded area ( its the area minus the seven smaller circles )
b) what fraction of the large conduit is occupied by the seven smaller conduits? - this seems to be like The entire circle area over the seven smaller ones

Diagram.jpgSo how would i do part a) without the radius of the smaller circles?

** i apologize for posting twice once in pre calc forum and once here but i accidentally posted in that forum**
 

chiro

MHF Helper
Sep 2012
6,608
1,263
Australia
Hey Gurp925.

By symmetry you will have a hexagon where the end points are tangent to both the large and smaller circles.

If you drew lines going from the center of the large and inner circle to the hexagon points then the length would be 1.5 times the radius of the smaller circle.

This will give you a relationship for the radii and also can be used to find areas.