In both pictures, the circle has radius .
Find the ratio of the shaded area in (i) to the shaded area in (ii).
Answer in the form 1 : , where is a decimal to 3 significant figures.
(i) Area of square = $4r^2$, area of circle = $r^2$, shaded area = $4r^2 - r^2$
(ii) Area of circle = $r^2$, area of square = $2r^2$, shaded area = $r^2 - 2r^2$
Going round in "circles" here to determine the ratio of these seemingly disparate fractions; any ideas?
Compare shaded area areas directly:
$\frac{4r^2 - r^2}{r^2 - 2r^2} = \frac{4 - }{ - 2} = 0.752$
Ratio 1 : 0.752
To avoid possible confusion plot the areas together on either side of common circle periphery
Considering area outside and inside of the circle radius $r$ their ratio
$$ \frac {A_{outgreen}}{A_{inyellow}}= \frac {4r^2- \pi r^2}{\pi r^2- (\sqrt 2 r )^2}= \frac {4-\pi}{\pi-2}=0.751938 $$