The diameters of two silver discs are in the ratio 2:3 . What Will be the ratio of their areas

Given:

The diameters of two silver discs are in the ratio 2:3.

To do:

We have to find the ratio of their areas.

Solution:

Let the radius of the two discs be $r_1$ and $r_2$.

We know that,

Area of a circle of radius $r=\pi r^2$

Therefore,

Ratio of the diameters $=2r_1:2r_2$

$\Rightarrow r_1:r_2=2:3$

Ratio of the areas of the circles $=\frac{22}{7} \times(r_1)^{2}:\frac{22}{7} \times(r_2)^{2}$

$=r_1^2:r_2^2$

$=(\frac{r_1}{r_2})^2$

$=(\frac{2}{3})^2$

$=\frac{4}{9}$

The ratio of the areas of the discs is $4:9$.