Question

If the radius of a circle is decreased by 20%, find the percentage decrease
arca:
A 36%
32%
C. 21%
D. 42%​

Answer 1

Area of circle= πr^2=22/7 r^3= 3.1426 r^2

When,

Radius is decreased by 20%,

Radius

= r -20/100*r

=4r/5

After decrement in radius,

Area

=πr^2

=22*16r^2/7*25

=352r^2/ 175

=2.0114r^2

Area = A1-A2/ A1 *100%= 36%

Answer 2

The percentage decrease area is $\ 36\%$ and option (A) is correct.

Step-by-step explanation:

Given:

The radius of a circle is decreased by 20%.

To Find:

The percentage decrease area.

Solution:

Let the radius of original circle is p.

Area of original circle $=\pi p^{2}$

As given,the radius of a circle is decreased by 20%.

Radius of new circle q $=p-p\times\frac{20}{100}$

                                      $=\frac{80}{100}p$$=\frac{80}{100}p=\frac{4}{5} p$

Area of new circle $=\pi q^{2}$

                               $=\pi (\frac{4}{5}p )^{2}$

                                $=\frac{16}{25} \pi p^{2}$

 Decrease in area  $= \pi p^{2} -\frac{16}{25} \pi p^{2}$

                                $=\pi p^{2} (1-\frac{16}{25} )$

                               $=\frac{9}{25} \pi p^{2}$

Percentage decrease in area $=\frac{\frac{9}{25}\pi p^{2} }{\pi p^{2} }\times100$

                                                   $=36 \%$

Thus,the percentage decrease area is $\ 36\%$ and option (A) is correct.

                                                           

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