Question

The diameter of two silver discs are in the ratio 2:3 . what will be the ratio of their areas?

Answer 1

Ratio of diameters of 2 discs = 2:3 = 2d/3d

So, ratio of radius will be the same,

As, ( 2d/2) / (3d/2) = 2:3 = 2r /3r

=> area of smaller disc = pi ( 2r)²

& area of larger disc = pi ( 3r)²

=> ratio of areas = (pi 4 r² ) / ( pi 9 r² )

= 4:9

Answer 2

Answer ⬇️

As radius is 1/2 diameter, the ratio of the radii of the two circles will also be 2:3.

Let the radii of two circles be 2x and 3x respectively.

Area of first circle:

$\pi(2 {x}^{2} )$

Area of second circle:

$\pi(3 {x}^{2} )$

Ratio of the area of both circles:

$\frac{\pi( {2x}^{2}) }{\pi(3 {x}^{2}) }$

$= \frac{4 {x}^{2} }{9 {x}^{2} }$

$= \frac{4}{9}$

Hence ,the ratio of areas of two circular discs are 4:9.