ABC26GN4650 · Area
Subject: General Aptitude · Chapter: Area · Exam: · Marks: · Difficulty:
If the radius of a circle is increased by 6\%, then the area is increased by
(a)6\%
(b)12\%
(c)12.36\%
(d)16.64\%
Answer
Explanation
Let the original radius be R cm. $$\begin{aligned} & \text { New radius }=\left(\frac{106}{100} R\right) \mathrm{cm}=\left(\frac{53 R}{50}\right) \mathrm{cm} . \\ & \text { Original area }=\pi R^{2} . \\ & \text { Increase in area }=\pi\left(\frac{53 R}{50}\right)^{2}-\pi R^{2}=\pi R^{2}\left[\left(\frac{53}{50}\right)^{2}-1\right] \\ & \qquad=\frac{\pi R^{2}\left[(53)^{2}-(50)^{2}\right]}{2500}=\frac{\pi R^{2}(103 \times 3)}{2500} \mathrm{m}^{2} . \\ & \text { Increase } \%=\left(\frac{\pi R^{2} \times 309}{2500} \times \frac{1}{\pi R^{2}} \times 100\right) \%=12.36 \% . \end{aligned}$$
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