# Circles Homework 15 840

Smartandfun - Thanks for your question. I think I can help both you and your daughter. First, let's talk about Area. The Area of anything (circle, square, triangle, etc.) is always in terms of units squared. For example, a square where each side is 2inches has a perimeter (distance around) of 8inches and an area of 4inches squared. It's squared because we multiplied 2inches X 2 inches which = 4inches squared.

In example #4 the "m" simply represents the units (i.e. meters). It is "m squared" since the 78.5 represents the Area of the circle, and Area is always units squared.

I don't know the type of measurement (units) for your daughter's specific math problem, but whatever it is,those units would also squared.

But let's not get hung up on the units. What we know is that the Area of the circle is 200.96 and we want to figure out the circumference. If you look at the equations for the Area of a circle and the Circumference of a circle, they both have r (radius) in them. So if we could figure out the radius of the circle knowing the Area, then we could plug the radius of the circle into the Circumference equation in order to find the circumference.

So let's do that. We will let ?=3.14 to solve the problem:

step 1: A=2(?)r ^squared

step 2: 200.96 = ?r ^squared

step 3: 64=r ^squared (divide both sides of equation by 3.14)

step 4: 8=r (take the square root of both sides of the equation)

Now that we know the radius of the circle is 8 units we can substitute 8 for r into the circumference equation as follows:

C=2?r

C= 2?8 (we know r = 8 so plug it into the equation)

C=16? (multiple 2 X 8 to get 16)

C=16(3.14) (let ? = 3.14 to solve)

C=50.24units

Therefore, a circle with an Area of 200.96 units^squared has a radius of 8 units and a Circumference of 50.24 units.

I hope this helps. Thanks for asking.

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