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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Updated on: 10-Oct-2022

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