Please Help!
- Thread starter Madu
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Otis
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Hi Madu. I'd like to help, but I don't know what you need because you didn't say. The area formula for a circle is:
Area = (Pi)(radius2)
I would begin by using that formula to write the expression for each circle's area and simplify. (Note: In this exercise, symbol r does not mean radius.) The radius of the small circle is r/2. The radius of the large circle is 2r.
The difference between the two areas is the "area of the remaining portion", so you need to subtract the smaller area from the larger area.
The last step is to simplify the algebraic ratio [area of small circle]/[area of remaining portion].
Please show your work, so that tutors may see how far you've gotten. Thanks!
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Otis
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Hi Madu. The very first step is to obtain an expression that represents the area of the small circle. We do that by substituting the given expression for the small circle's radius, in the area formula that I gave you. Please let us know, if you've never seen substitution before.
I'll show you the steps for the small circle. Then, see if you can do the substitution and simplification for the big circle. I will show exponents, using the caret symbol (^). I will show multiplication, using an asterisk (*).
Area = Pi * (radius)^2
For the small circle, we're told radius = r/2
Therefore, we substitute r/2 for radius, in the area formula:
Area = Pi * (r/2)^2
Next, we simplify (that is, we square r/2):
Area = Pi * r^2/4
Please make an attempt to find the area for the big circle and simplify, using 2r for the radius instead of r/2.
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Otis
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I'm not sure what happened to Madu, but we hope they figured it out. So far, we've found an expression for the area of the small circle:
1/4 * Pi * r^2
The big circle has radius 2r, so its area is:
4 * Pi * r^2
After removing the small circle from the big circle, the remaining area is the difference:
4 * Pi * r^2 - 1/4 * Pi * r^2
That simplifies to 15/4 * Pi * r^2
Therefore, the ratio of the small area to the remaining area is:
(1/4 * Pi * r^2) : (15/4 * Pi * r^2)
We see the second value in that ratio is 15 times larger than the first value, so the ratio can be written as 1:15
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1/4 * Pi * r^2
The big circle has radius 2r, so its area is:
4 * Pi * r^2
After removing the small circle from the big circle, the remaining area is the difference:
4 * Pi * r^2 - 1/4 * Pi * r^2
That simplifies to 15/4 * Pi * r^2
Therefore, the ratio of the small area to the remaining area is:
(1/4 * Pi * r^2) : (15/4 * Pi * r^2)
We see the second value in that ratio is 15 times larger than the first value, so the ratio can be written as 1:15
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