It circumference of a circle is decreased by 50%, find the percentage decrease in its area.
A. 50%
B. 55%
C. 65%
D. 75%
E. None of these
Solution(By Examveda Team)
Cercumference of the circle is given by, 2* Pi * R.
Where 2 and value of Pi is constant. It means cercumference decreaases 50% only due to 50% decrease in radius.
Let original radius = R.
Original circle area = Pi * R*R = 3.14 *R *R.
Second radius = R/2.
Area = Pi * R/2 * R/2 = (3.14 *R *R)/4
Difference in area = 3.14 *R *R. - (3.14 *R *R)/4. = 2.35 *R *R
% change in area =[ ( 2.35 *R *R) *(100)] / (3.14 *R *R.) = 75%.
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