# Relationship of area to circumference

### Math Forum - Ask Dr. Math

Label the diameter and radius of a circle and describe the relationship between them. Recall and apply the formula for the circumference and area of a circle to. Understanding the Area and Circumference of a Circle. Factoid: The Now think about the area of the circle in relationship to the area of the square. Obviously. My 6th grade daughter asked if there is a shortcut for converting from area to circumference and back without finding the radius.

Okay, let's do a formula. The line from one side of the circle to the other is called the diameter. It is usually abreviated as d.

## Relationship between the radius, diameter, circumference, and area of a circle.?

The length of the side of the square is also d 2. The area of the square is d squared d times dand 3. The area of the circle is.

Circumference of a Circle - pdl-inc.info - Math Help

The circumference of the circle is just a percentage of the circumference perimeter of the square, and it's the same percentage no matter what the size. Believe it or not, that percentage is A seemingly random number is the answer to two different problems. Mathematicians and Pi Maybe you would want to give this ratio, which is approximately I will call it cake. I used to call it pie. Then the formula for the area of a circle is exactly cake times d squared.

If we divide both sides by two pi, to solve for r, what are we left with? Well we have an r on the right hand side, we have r is equal to pi divided by pi, that's just one. Six divided by two is three. So we get that our radius, right over here, is equal to three units. And then we can use the fact that are is equal to pi, r squared, to figure out the area.

This is going to be equal to pi times three squared. Oh and you have to write parenthesis there. Pi, times three, squared, which is of course going to be equal to nine pi. So for this particular example, when the circumference is six pi units, we're able to figure out that the area, this is actually going to be nine pi square units, or I could write units squared.

Cause we're squaring the radius. The radius is three units, so you square that, you get the units squared.

Now let's see if we can come up with a general formula. So we know that circumference is equal to two pi r. And we know that area is equal to pi r squared.

## You need to have JavaScript enabled in order to access this site.

Can we come up with an expression or a formula that relates directly between circumference and area? And I'll give you a hint, solve for, you could solve for r right over here, and substitute back into this equation, or vice versa. Pause the video, see if you can do that.

• Understanding the Area and Circumference of a Circle
• Area and circumference of circles

However, my answer to the area question for this circle has to be 3. Still haven't figured out how this fits in.

### Circle: Area and Circumference

She's thinking like a mathematician. Why keep solving special cases of the same problem over and over, if you can just solve the general case one time and be done with it? In the long run, she'll probably learn more from your willingness to jump in and play around and look for the answer, than from actually finding the answer itself. It's that kind of playing around that kids are supposed to be learning in their math classes, but it hardly ever works out that way.

That's a good intuition. It might be more helpful than you think.

### Relationship between the radius, diameter, circumference, and area of a circle.? | Socratic

But let's set that aside for now. Again, it might be more helpful than you think. Let's go back to where your daughter started: