Difference between revisions of "2023 AMC 8 Problems/Problem 12"

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First the total area of the <math>3</math> radius circle is simply just <math>9* \pi</math>. Using our area of a circle formula.
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Now from here we have to find our shaded area. This can be done by adding the areas of the <math>3</math> <math>\frac{1}{2}</math> radius circles and add then take the area of the <math>2</math> radius circle and subtracting that from the area of the <math>2</math>, 1 radius circles to get our resulting complex area shape. Adding these up we will get <math>3 * \frac{1}{4} \pi + 4 \pi -\pi - \pi = \frac{3}{4} \pi + 2 \pi = \frac{11}{4}</math>
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==Animated Video Solution==
 
==Animated Video Solution==
 
https://youtu.be/5RRo6pQqaUI
 
https://youtu.be/5RRo6pQqaUI
  
 
~Star League (https://starleague.us)
 
~Star League (https://starleague.us)

Revision as of 19:29, 24 January 2023

First the total area of the $3$ radius circle is simply just $9* \pi$. Using our area of a circle formula.

Now from here we have to find our shaded area. This can be done by adding the areas of the $3$ $\frac{1}{2}$ radius circles and add then take the area of the $2$ radius circle and subtracting that from the area of the $2$, 1 radius circles to get our resulting complex area shape. Adding these up we will get $3 * \frac{1}{4} \pi + 4 \pi -\pi - \pi = \frac{3}{4} \pi + 2 \pi = \frac{11}{4}$


Animated Video Solution

https://youtu.be/5RRo6pQqaUI

~Star League (https://starleague.us)