anonymous
  • anonymous
PLEASE HELP! The radius of large circle is R cm and the radius of small circle is r cm. Each small circle is equal in area to the shaded region. Find R^2: r^2. Picture attached below!
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
1 Attachment
Mertsj
  • Mertsj
\[\frac{R^2}{r^2}=\frac{10}{1}\]
anonymous
  • anonymous
How did you arrive at this answer? :O Could you please explain a little?

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Mertsj
  • Mertsj
The area of the large circle is pi R^2 Since the small circle = the shaded area and the shaded area + the small circle = 1/5 of the circle, we have 2 times the area of the small circle = 1/5 of the large circle. But the area of the small circle is pi r^2. So: \[2\pi r^2=\frac{1}{5}\pi R^2\]
Mertsj
  • Mertsj
\[10\pi r^2=\pi R^2\]
Mertsj
  • Mertsj
Divide both sides by pi r^2
Mertsj
  • Mertsj
\[\frac{10\pi r^2}{\pi r^2}=\frac{\pi R^2}{\pi r^2}\]
anonymous
  • anonymous
Ok! Thank you so much! YOU ROCK! :D
Mertsj
  • Mertsj
\[\frac{10}{1}=\frac{R^2}{r^2}\]
Mertsj
  • Mertsj
yw
anonymous
  • anonymous
The area of the large circle is pi R^2 Since the small circle = the shaded area and the shaded area + the small circle = 1/5 of the circle, we have 2 times the area of the small circle = 1/5 of the large circle. But the area of the small circle is pi r^2. So: 2πr2=15πR2 i dont understnd this?
Mertsj
  • Mertsj
It is given that the shaded area is equal to the area of the small circle. Do you see that? Also we see from the picture that the big circle is divided into 5 equal part. So shaded area + small circle = 1/5 large circle. Now substitute the small circle for the shaded area in the equation above. small circle + small circle = 1/5 large circle 2 times the small circle = 1/5 large circle \[2 pi r^2=\frac{1}{5} pi R^2\]

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