MCQ

If the radius of a circle is diminished by 10%, then its area is diminished by

#### Options

10%

19%

20%

36%

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#### Solution

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% .

Concept: Area of Circle

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