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Question
If the radius of a circle is diminished by 10%, then its area is diminished by
Options
10%
19%
20%
36%
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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