Answer 1

Let x be the initial radius of the circle.

Therefore, its area is`pix^2` ……..(1) 

It is given that the radius is diminished by 10%, therefore, its new radius is calculated as shown below,

new radius=`x-0.10 x`

`∴ "new radius "=0.90x`

`∴ "new radius "=(0.90 x)^2`

`∴ "new radius "= 0.81 x^2`

Now we will find the percentage decreased in the area. 

`∴ "change" = 0.81 x^2-x^2` 

`∴ "change" = 0.19 x^2` 

Therefore, its area is diminished by 19% .