Question

The circumference of a circle is 31.4 feet. What is the area of the circle? Explain how you found your answer.

Answer 1

First off you will need to know the formula for the area of a circle, which is A=pi*radius*radius.

next you will need to know the formula for the circumfrence of a circle, which is 2*pi*r=Circ.

You know that circumfrance is equal to 31.4 feet, so set that equal to the equation for circumfrence to find r.

\[31.4 ft = 2*3.14*r\]
because pi is equal to 3.14. Multiply 3.14 by 2 to get 6.28.

31.4 ft = 6.28*r

divide 31.4 by 6.28 and you will get r.

5 ft = r.

you will then take that information and put it into the equation to find the area:

A=pi*r*r
A=pi*5*5

can you figure out Area from there?

Answer 2

no..I do not understand. Sorry

Answer 3

thats fine, the only i can help you more is if you tell me if you dont understand.

Ok so you are looking for area, and the formula for the area of a circle is always:

Area= pi*radius*radius.

but you are given circumfrance. do you have it up until there?

Answer 4

yes

Answer 5

ok, you are given the circumference of the circle, at 31.4 feet. The formula for the circumference of a circle is always C=2*pi*r.

and you are given circumference, so set the equation to the value given to give you the formula:

31.4 feet = 2* pi * radius.

Are we clear up until here?

Answer 6

yes

Answer 7

ok, so we need to solve for radius because that is what we need for the equation of area.
both 2 and pi are constants, so we can multiply pi by 2, and divide 31.4 feet by the product of 2 and pi, so the work will look like this:

31.4 feet = 2*pi*radius
31.4 feet = 6.28* radius (6.28 because has an accepted working value at 3.14)

now divide 31.4 by 6.28

5= radius.


Clear up until this point?

Answer 8

yes :)

Answer 9

ok, so you now know that the formula for area is A=pi*radius*radius.

Solve for area now that you solved for radius.

Can you figure this out?

Answer 10

pi *5*5 = 3.14 x 5 x 5 = 81 ?

Answer 11

not quite, you have the equation set up right, i would just punch that back into a calculator, because i am getting a number that is close to that, but not exactly

Answer 12

Not using a calculator...lol

Answer 13

78.5 my mistake...lol

Answer 14

So that is my answer? 78.5?

Answer 15

yes, the answer is 78.5

Answer 16

and if I needed the diameter I would divide in half?

Answer 17

nope, diameter is two times the radius. so you would multiply by 2

Answer 18

but the formulas do not use diameter, so if you are given diameter, you must divide diameter by 2 to get the radius. dont use diameter when you have to use radius

Answer 19

ok. Thanks. That's helped alot. Have to go to bed now. Big test tomorrow. Wish me luck :) Have a great night :)