Question

If the radius of a circle is diminished by 10%, then its area is diminished by:

1. 10%

2. 19%

3. 20%

4. 36%

Answer 1

Let the initial radius if the circle be r1 and initial area be a1.

Area of circle(a1) = π X r1^2

Now, final radius(r2) = 90% of r1

..because 10% is reduced........

r2 = 9 r1 / 10

Let the new area be a2

a2 = π r2^2 = π {9r1/10}^2

Increase in area = a1/a2 = π r1 r1 / π 9r1/10 9r1/10

= 1 / 9/10 * 9/10 = 1 / 81/100 = 100/81

or 100/81 * 100 % = 123.456%

Decrease in area(%)
= 123.456 - 100 = 23.456 % = 20% approx.......................

Answer 2

Answer:

Explanation:

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