Question

The area of a circle is doubled when its radius $r$ is increased by $n$. Then $r$ equals:

• A. $n(\sqrt{2}+1)$
• B. $n(\sqrt{2}-1)$
• C. $h$
• D. $n(2-\sqrt{2})$
• E. $\frac{n\pi }{\sqrt{2}+1}$

Answer 1

Answer: (A)

$n(\sqrt{2}+1)$

$A=\pi r^{2}2A=\pi {(r+n)}^{2}2\pi r^2=\pi (r^2+n^2+2nr)r^2=n^2(1+2n)r=n(1+\sqrt{2})$