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If the Radius of a Circle is Diminished by 10%, Then Its Area is Diminished by - Mathematics

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% .

 

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APPEARS IN

RD Sharma Class 10 Maths
Chapter 13 Areas Related to Circles
Q 15 | Page 70
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