Question

Social distancing guidelines state that we must stay a minimum of 6ft away from each other. How many circles with a 3ft radius could fill a 100 square foot (10ft x 10ft) space without overlap?

*Tip*
Area of a Circle = π r​ ​where r=radius

Answer 1

Given:

The radius of each small circle = 3 ft

The area of the given space = 100 ft

To find the number of circles could fill the space of 100 ft.

Formula

The area of a circle is

`A = \pi r^(2)`, where r be the radius of the circle.

Now,

Putting, r = 3 and π = 3.14 we get,

`A = (3.14)(3^(2) )` sq ft

or,
`A = 28.26` sq ft

So, the area of each circle is 28.26 sq ft

Now,

Number of circles that could fill into the given space = 100÷28.26

= 3.53≈3

Hence,

3 circles with radius 3 ft could fill a 100 sq ft space without overlap.