1. If the circumference of a circle is decreased by 50% then the percentage of decrease in its area is:
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By: anil on 05 May 2019 02.01 am
As we know circumference of a circle will be directly proportional to its radius $$r_{1}$$
hence when it got half its radius will also get half
now area of a circle is directly proportional to square of its radius
hence when its radius gets half its area gets $$frac{1}{4}$$th of its value
let us say area was A
after decrement it will be $$frac{A}{4}$$
Decrement is of $$frac{3A}{4}$$ which is 75% of its original value.
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hence when it got half its radius will also get half
now area of a circle is directly proportional to square of its radius
hence when its radius gets half its area gets $$frac{1}{4}$$th of its value
let us say area was A
after decrement it will be $$frac{A}{4}$$
Decrement is of $$frac{3A}{4}$$ which is 75% of its original value.