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KEAM 2010 Math Paper

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Question : 41 of 120

Marks: +1, -0

If the error committed in measuring the radius of the circle is

0.05\ \%,

then the corresponding error in calculating the area is

$0.05\ \%$
$0.0025\ \%$
$0.25\ \%$
$0.1\ \%$
$0.2\ \%$

Solution:

Let the radius of circle be 100 unit.

Then, area of circle

=10000\pi

sq unit

The error in the radius is

0.05\ \%

Therefore, new radius is 100.05 unit.

∴ New area

=10010.0025\ \text{sq}

unit

∴ Error in area

=\frac{10010.0025\pi-10000\pi}{10000\pi}\times 100\ \%

=\frac{10.0025}{10000}\times 100\ \%

=0.1\ \%

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