Subject: General Aptitude · Chapter: Area · Exam: · Marks: · Difficulty:
If the radius of a circle is decreased by 50\%, find the percentage decrease in its area.
Answer
Answer (as printed):
Explanation
Let original radius $=R$. New radius $=\frac{50}{100} R=\frac{R}{2}$. Original area $=\pi R^{2}$ and New area $=\pi\left(\frac{R}{2}\right)^{2}=\frac{\pi R^{2}}{4}$. ∴ Decrease in area $=\left(\frac{3 \pi R^{2}}{4} \times \frac{1}{\pi R^{2}} \times 100\right) \%=75 \%$.
Explanation as extracted from the printed page; notation may be imperfect.