Circles in a square

Question

1. You have a square that is 5cmx5cm.
2. You must fit 5 circles inside this square.
3. All of the circles have the same diameter.
4. What is the highest possible radius of the circles?

Answer 1

put 3 circles in a vertical line and put 3 circles in a horizontal line

there are only 5 circles because 1 circle is in the middle common to both lines

the square is 5 cm by 5 cm

5/3 cm will be the length of each diameter of each of the 3 circles

the radius of each circle will be (1/2)(5/3)=5/6 cm or 0.8333... cm

Answer 2

Hi Jonathan,

 

You would want to fit the circles along the diagonal since that is the longest segment within the square.

According to Pythagorean theorem, the lenght of diagonal, d, will be

d = √(5^2 + 5^2)

= 5√2 cm

Divide this by 5 to get the diameter length of one of the circles.

diameter = 5√2 / 5

= √2 

then the highest possible radius will be r=√2/2 cm