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The diameters of two circles are 3.5 cm and 4.2 cm. Find the ratio of the area of the small circle to that of the bigger circle.
Given:
The diameters of two circles are 3.5 cm and 4.2 cm.
To do:
We have to find the ratio of the area of the small circle to that of the bigger circle.
Solution:
We know that,
Area of a circle of radius $r=\pi r^2$.
Radius of first circle $=\frac{3.5}{2}\ cm$
Radius of second circle $=\frac{4.2}{2}\ cm$
The ratio of the area of the small circle to that of the bigger circle $=\pi (\frac{3.5}{2})^2:\pi (\frac{4.2}{2})^2$
$=\frac{(3.5)^2}{4}:\frac{(4.2)^2}{4}$
$=12.25:17.64$
$=1225:1764$
$=49\times25:49\times36$
$=25:36$
The ratio of the area of the small circle to that of the bigger circle is $25:36$.
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