| If the radius of circle is increased by 50%, then what will be the percentage increase in its area? |
A) 125%
B) 100%
C) 50%
D) 75%
E) None of these
Correct Answer: A
Solution :
| Area of circle \[=\pi {{r}^{2}}\] |
| New radius \[=r+\frac{50}{100}r=\frac{3r}{2}\] |
| New area \[=\pi {{\left( \frac{3r}{2} \right)}^{2}}=\frac{9\pi {{r}^{2}}}{4}\] |
| \[\therefore \]Increase percentage\[=\frac{\frac{9\pi {{r}^{2}}}{4}-\pi {{r}^{2}}}{\pi {{r}^{2}}}\times 100\]% |
| \[=\frac{5\pi {{r}^{2}}}{4\,\times \,\pi {{r}^{2}}\,}\,\times 100\]%=125% |
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