Bigger, but how big? [Circles III]
How big is the red portion's area compared to the blue portion's area (only the closed broken-donut shape)? All angles that look perpendicular can be assumed as perpendicular, all lines that look like an unbroken line is a proper line, and all arcs that look like part of a circle, are part of a circle.
Type the comparison as a decimal, if it is 5 2 , type it as 0 . 4 0
Type recurring decimals with two decimal places. 7 1 can be typed as 0.14
It is the ratio of comparison, not the difference
Report area : The report room
The answer is 0.33.
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3 solutions
Sometimes(rarely for me), even difficult ones are fun!
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I just posted this as a explanation as I have nothing to explain!
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Explanation Paradox?
\[ \begin{align} {\color{Red}{A_{\text{Quarter circle}}}} &= \dfrac{\pi x^2}{4} \\ \\ {\color{Blue}{A_{\text{Quarter donut}}}} &= \dfrac{\pi (2x)^2}{4} - \dfrac{\pi x^2}{4} \implies \dfrac{3 \pi x^2}{4} \\ \\ \dfrac{{\color{Red}{A_{\text{Quarter circle}}}}}{{\color{Blue}{A_{\text{Quarter donut}}}}} &= \dfrac{\frac{\pi x^2}{4}}{ \frac{3 \pi x^2}{4}} = \dfrac{1}{3} \approx \boxed{0.33}
\end{align}\]
A simple solution for a simple question. Thanks @Mahdi Raza !
Colorful solution! :)
Area of red = 4 π x 2
Area of blue = 4 π ( 2 x ) 2 − 4 π x 2 = 4 π ( 4 x 2 ) − 4 π x 2 = 4 π ( 3 x 2 )
Ratio of red to blue = 4 π ( x 2 ) ÷ 4 π ( 3 x 2 ) = 3 1 ≈ 0 . 3 3 (to 2 decimal places).
Thanks for trying out my question @Vinayak Srivastava !
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You're welcome! BTW, please add the word "ratio" as people might get confused!
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Added as you said. Thanks for the helpful suggestion!
Fun questions are not in the difficulty, but in the simplicity