hard maths question (1 Viewer)

[kooltrainer]

Question: find the value of r (radius) for which the area sum of the 5 circles is a minimum.

note: - the four circles in the corner are equal.
- r<x

 

[tommykins]

Do we do it in terms of x ? or what, frmo that I don't think we can a numeric value.

 

[vulgarfraction]

sum areas:

middle circle of radius r

little circles: (rt2x-r)/(1+rt2)

(You can get that because, since your little circles have the same radii, the points joining their centres are a square, and the line joining little centres to big centre are equal (sum of two radii), you get 4 congruent triangles so the angles at the centre are 90. So those lines are the diagonals of the smaller square.)

Then differentiate the area wrt r.

tommykins- obviously.

 

[kooltrainer]

cool, but wots t ? is it radius of smaller circles?

 

[vulgarfraction]

cool, but wots t ? is it radius of smaller circles?

Sorry- (rt) meant square root of. My bad.