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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 ispix^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% .

Is there an error in this question or solution?
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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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