rebecca1233
] The radius of a circle is multiplied by 10. Its area is _____ times bigger than the original circle.
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rebecca1233
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@Mertsj Can you guide me please
rebecca1233
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@mathteacher1729
Mertsj
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Lets make two circles. Let the radius of the first one be 1 and the radius of the second one be 10.
rebecca1233
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alright
Mertsj
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|dw:1362242349336:dw|
Mertsj
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What is the area of the first circle? Just leave your answer in terms of pi.
Mertsj
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What is the area of the second circle? Again, leave your answer in terms of pi.
rebecca1233
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but thats not what its asking for
so the answer is 10
Mertsj
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No, sweetheart. Just answer my questions. I'm trying to help you understand so you don't have to do so much work on the next problem you have that is similar to this one.
rebecca1233
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so the first one is 1
rebecca1233
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wait do i just do 10*10 cause its 10 times bigger that will give me 100
Mertsj
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rebecca1233
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3.14 (1)
Mertsj
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What is the area of the second circle? Don't use 3.14. Just leave your answer in terms of pi
rebecca1233
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10
rebecca1233
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ii ( 10)
Mertsj
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|dw:1362242645972:dw|
rebecca1233
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alright so what next
Mertsj
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So do you see that to find how many times bigger the second circle is we should divide the area of the second circle by the area of the first circle?
rebecca1233
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so the area of the first circle is 1
Mertsj
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Please look at the drawing I made. For the little circle, it says A = what?
rebecca1233
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pie
Mertsj
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And the area of the big circle is what?
rebecca1233
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100pie
Mertsj
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And what is 100 pi divided by pi ?
rebecca1233
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100 / 3.14
Mertsj
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|dw:1362242866060:dw|
rebecca1233
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100
rebecca1233
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when i divide a 100 by pie i get a decimal
Mertsj
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rebecca1233
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it equals 100
Mertsj
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Do you understand so far because here is the important part which will save you work in the future?
rebecca1233
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yes. i get it :) Thanks. can you help me with a few more questions im stuck on
rebecca1233
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please
Mertsj
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Wait. I want to teach you the general principle of the problem we just did.
rebecca1233
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oh ok
Mertsj
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In finding the area of a circle, what do you do with the radius?
Mertsj
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You square the radius don't you?
rebecca1233
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yes
Mertsj
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So, if we make the radius 10 times bigger and then square it, since 10 squared is 100, the new circle will be 100 times bigger. Do you understand that?
rebecca1233
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yes