+0  
 
+1
101
1
avatar+186 

Can someone please help me with this?

 

Four circles are drawn. Let A1, A2, A3, A4 be the areas of the regions, so A1 is the area inside the smallest circle, A2 is the area outside the smallest circle and inside the second-smallest circle, and so on. The areas satisfy A1 = A2/2 = A3/3 = A4/4. Let r1 denote the radius of the smallest circle, and let r4 denote the radius of the largest circle. Find r4/r1.

 

Asymptote code below

[asy]
unitsize(1 cm);

pair[] O;
real[] r;

O[1] = (0,0);
O[2] = (0.1,0.2);
O[3] = (-0.2,-0.1);
O[4] = (0.1,-0.3);

r[1] = 1;
r[2] = 1.5;
r[3] = 2;
r[4] = 2.5;

fill(Circle(O[4],r[4]),lightblue); draw(Circle(O[4],r[4])); label("$A_4$", (1.8,-1.5));
fill(Circle(O[3],r[3]),lightgreen); draw(Circle(O[3],r[3]));label("$A_3$", (-1.3,-1.3));
fill(Circle(O[2],r[2]),yellow); draw(Circle(O[2],r[2]));label("$A_2$", (1,1));
fill(Circle(O[1],r[1]),lightred); draw(Circle(O[1],r[1]));label("$A_1$", O[1]);
[/asy]

 

 

Thank you so much!

 Jun 6, 2020
edited by Caffeine  Jun 6, 2020
 #1
avatar
0

From the given information, r_4/r_1 = 1 + 2 + 3 + 4 = 10.

 Jun 6, 2020

29 Online Users

avatar
avatar