Question

If the circumference of the circle is reduced by 50%, then by how much per cent area of the circle reduced? Explain with an example.

Answer 1

Let initial radius = r unit.
∴ Initial circumferance = 2πr unit.
∴Initial area = πr² sq unit.
Now, final circumference = 2πr - 50% of 2πr = πr unit.
let final radius be 'a' unit.
∴ 2πa = πr.
⇒a = r/2.
∴ Final area = πa² = πr²/4 sq unit.
∴ Reduction in area= (πr²-πr²/4)/πr²*100 = 75%.(Ans.)
All the best !!!