Question

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

Answer 1

Here's your answer !!


Solution:-

Diameter of two silver discs are in ratio 2:3 .

Let it be 2x and 3x respectively!



Since we know that ,

$= >radius\: = \frac{diameter}{2}$


So,

Radius of 1st silver discs =

$= > \frac{2x}{2} = x$


And radius of 2nd silver discs=

$= > \frac{3x}{2}$



We know that area of circle =
$= > \pi {r}^{2}$


Therefore,


Area of 1st disc =
$= > \pi {x}^{2}$


Area of 2nd disc =

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


Ratio of area of both circle :

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


$= > \frac{\pi {x}^{} }{\pi (\frac{9x}{4}) }$


$= > \frac{4}{9}$

Hence, Ratio of area of two circular disc are 4:9



Hope it helps you!! ^^

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