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I need help on finding the Circumference and Area of Circles.

I  need help on this, my math teacher is not a very good teacher when it comes to teaching. Please explain this to me. This > π < is the pi symbol. Thanks!

Solve using:        C = 2πr = πd   or      A = πr2

  1. What is the circumference of a circle with a radius of 6?
  2. The circumference of a circle is 24π. What is the radius?
  3. If the circumference of a circle is 32π, what is the area?
  4. What us the area of a circle with a radius of 5?
  5. The area of a circle is 169π. What is the radius?
  6. The area of a circle is 100π. If the radius is doubled, what is the new area?

 

Comments

Hey Courtney... Apparently the Answer section below isn't working...

p is just a definition: it's the ratio between a circle's diameter and its circumference.  In other words, any circle circumference is approximately 3.14 (p) times longer (around) than its diameter length.  Some old Greek dude discovered it a few thousand years ago...  Let's do the first 3 problems together - by then I think you'll have confidence you can do the remaining 3!

1.  If C = 2pr, then we substitute C = 2*3.14*6, = 37.68

2.  If C = 2pr, then let's rearrange that so we can find r:  divide both sides (to keep it equal) by 2p to get r by itself: C/2p = 2pr/2p, so r = C/2p.  Now substitute:  r = 24p/2p = 12

3.  If C = 2pr, then r = C/2p  (see #2 above), then r = d/2.  

If A = pr2, then A = p (C/2p)2.  Substitute:  A = p (32p/2p)2, or A = p (16)2

A = 3.14 * 256 = 803.84

Now can you complete #3 - #6?  I bet you can...   :-)

I tried adding answers via Answers below, and also via Comments - no go!

Amazing! I was 10 yrs. old in Mexico and learned that Circumference = Diameter times pi(3.14).  So, if you have a circle with a diameter (from edge to edge) of 5 in. you X 3.14 =15.7 in. diameter. 
Now to find the area of a circle, you square (multiply the # by itself) X the radius  (from center to edge).  
So, as in the 1st. example the diameter was 5 in. the radius if 2.5 in. so 2.5 X 2.5= 6.25 in. X 3.14= 19.625 in.
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7 Answers

Courtney , to solve these you would substitute the formula for each.

Concepts to remember.
• The Circumference is the area around the outside of the circle.
• The Radius is a straight line from the center of the circle and the endpoint lies on the circle.
• The Diameter is a straight line through the center of the circle and both endpoints lie on the circle. Therefore the Diameter is twice the length or distance of the radius.
• pi π symbolizes the ratio -- the relationship with respect to relative size of the circumference of circle to its diameter. The numrical value of π is 3.14

Let's start with what we know and determine what we want to know.

• We know that the Circumference is equal to 2 times π times the radius. = 2(3.14) times the radius or (6.28 x the radius).
• We know that the Circumference is equal to π times the diameter or (3.14 x diameter.)
• We know that the area of a circle is π times the radius squared or ( 3.14 x r2).

Let's start with number 1.

1. The circumfererence is equal to "2 πr." We know 2 π= 6.28. The radius is 6.
The equation would be 6.28 x 6 = 37.68
2. The circumference is equal to "2 πr." If the circumference is 24 π then our equation would be " 24 π = 2 πr". To simplify divide both sides by π to eliminate. The equation becomes 24 = 2r. 12= r (radius).
3. The area is equal to πr2. The circumference is equal to "2 πr." If the circumference is 32 π then our equation would be " 32 π = 2 πr". To simplify divide both sides by π to eliminate. The equation becomes 32 = 2r. 16= r (radius).
Substitute 16 for r in our formula and 3.14 for π and we have
A= 3.14(162) = 3.14 x 256 = 803.84

If you follow the concepts outlined for the 1st 3, you should be able to compute the final 3.

 

C = 2πr = πd or A = πr2

What is the circumference of a circle with a radius of 6? 12π
The circumference of a circle is 24π. What is the radius? 12
If the circumference of a circle is 32π, what is the area? 18
What us the area of a circle with a radius of 5? 25π
The area of a circle is 169π. What is the radius? 13
The area of a circle is 100π. If the radius is doubled, what is the new area? π400

For each question, you have to:

1) Decide which formula to use.
2) Plug each number that's given into the right place in the formula.
3) Solve.

Here's how to do #1:

It's asking for circumference, so use the C = 2*pi*r formula.

Plug in "6" for the radius:  C = 2*pi*6

Solve:  C = 12*pi

Hi Courtney,

1.  Since the radius is 6 then r = 6 and the circumference is C = 2*pi*6 or 12*pi

2.  The circumference is 24pi so that must equal the equation for circumference or 24pi = 2*pi*r; You can divide both sides of the equation by 2pi so then r = 12

3.  Solve the same way as question 2, divide by 2pi to get r = 16 then plug into the equation for area.  A = pi*(16)2 = 256pi

4.  Plug in 5 for the radius; A = pi*(5)2 = 25pi

5.  if the area is 169pi set that equal to the equation for area so 169pi = pi*r2.  First divide both sides of the equation by pi so then r2 = 169 and then take the square root of 169 to get r = 13.

6.  First solve for the radius like in question 5 to get r = 10.  Now double the radius (20) and plug into the area equation A = pi*(20)2 = 400pi

Hope this helps!

The Circumference of a circle is the distance around the outside of it (think walking around the outside of a round pool). The circumference is equal to π times the twice the radius (the distance from the center of the circle to the outside) or the diameter (the distance from one side of the circle to the other, passing through the center of the circle).

Based on this,

1 : C = 2πr = 2π(6) = 12π

2: 24π = 2πr Divide each side by 2π and you are left with r = (24π )/(2π ) or r = 12

3: Follow the example in item 2. Once you find r, square it, then multiply by π, and you will have the area.

4: A = πr2 = π(5)2 = 25π

5: A = 169π, so 169π = πr2. Divide both sides by π (which leaves you with r2 on the right side), then take the square root of both sides.

6: Follow the steps in problem 5 to determine the radius of the circle with area 100π. Then square twice the radius, and determine your new area (Hint: It's A' = π(2r)2 )

π is simply a ratio between the diameter, d (or twice the radius, r) of a circle and it's circumference. In other words, a circle that has a diameter of 1 or a radius of 1/2 will have a circumference of π. π is conveniently also the ratio of r squared (r times r) to the area of the circle, meaning that a circle with radius 1 will have an area of π. Let's take a look at some of your questions.

1) Here we've been given that the radius 6. Now we simply plug that into our equation for circumference and we find a circumference of 12π or about 37.7.

2) Now we have the circumference of the circle and want the radius so we rearrange our circumference equation to solve for r. We do this by dividing both sides by 2π to get: r = C/2π. Now we just plug in our circumference of 24π to get 24π/2π or 12. 

3) We can solve this equation in three steps. First we use the equation from problem 2 to solve for the radius. Doing that will give us 16 as r. Now we plug 16 into our equation A = π(r-squared) to give us an area of 256π.

 

As you can see, all these questions can be solved by moving from what you are given (either the radius, the area, or the circumference) to what you need to solve. See if you can solve the next three problems on your own using what I have explained. For number 6, you need to solve for the original radius, double it, and then solve for the new area.  Hope that helps!

Ok, Courtney, it's not hard:  

We know that 2 r = 1 d (diameter is twice the radius), right? 

And you may remember, or can easily find, that pi (∏) = approximately 3.14

1.  We have C = 2∏r, or ∏d.   Now let's just substitute what we know:  2*∏*r = 2*3.14*6 = 37.68

2.  If C - 2∏r, then C/2∏ = r, or r = C/2∏:  r = 32∏/2∏ = 16

3.  If C = 32∏, then r = 16∏.  A=∏r:  A = (∏)(16∏)= 256∏3.  If we multiply that out, = 7,925.54

Now I know you can do the rest!