How can I make an experiment where you find the relationship between diamater and area of a circle?
The relationship being π(0.5d)^2

I was thinking getting a few circular items, placing them graphing paper, trace the circles, and count the approximate amount of squares within the circle.
But how will this get the person doing the experiment to finding π(0.5d)^2 ???

Question

How can I make an experiment where you find the relationship between diamater and area of a circle?
The relationship being π(0.5d)^2

I was thinking getting a few circular items, placing them graphing paper, trace the circles, and count the approximate amount of squares within the circle.
But how will this get the person doing the experiment to finding π(0.5d)^2 ???

campbell_st · Answer

I think the experiment is to is looking at the connection between linear measurement diameter and radius and then what happens with area. 

so find diameter of some round shapes 

find the area using $$A = \pi \times d^2$$

then find the area using d/2 ( or radius)

if you halve the diameter, what happens to the area...?

anonymous · Answer

The point is not use the area formula, but to find it. That's what has me stumped.

anonymous · Answer

The formula is the relationship, and the experiment should result in finding that relationship.

anonymous · Answer

@tabithax3

anonymous · Answer

@campbell_st 

any idea?

campbell_st · Answer

well I was thinking you could draw a square and then a circle inside the square and have the circumference touch the edge of the square. the draw a square inside the circle... and the area of the circle has to be between the 2 square areas. 

You could then use the formula you have.. d will be the side length of the larger square...? 

not sure if it helps

anonymous · Answer

I think I see what you're getting at, thanks.

campbell_st · Answer

actually thats the way Archimedes did it... just increased the number of sides... and said it had to be between the 2