Question

If the area of a circle is halved when its radius is decreased by n, then the radius is equal to

• A. $n(2+\sqrt{2})$
• B. $n(\sqrt{2}-1)$
• C. $n(3-\sqrt{2})$
• D. $n\sqrt{2}$

Answer 1

The correct option is A $n(2+\sqrt{2})$

Given that, the area of a circle is halved when its radius is decreased by $n$,

Assume that the circle has a radius $r$. Then, area of a circle $=\pi r^2$.

When the radius is reduced by n, then the new radius is $r-n$.

When the radius is r-n, then the area is the new area is $\pi (r-n{)}^2$

According to the given statement, when the radius is $r-n$, then the new area is half of the original value.

Thus, $\pi (r-n{)}^2=\pi r^2/2$

Solving this equation, $r=n(2+\surd 2)$.

Hence, this is the answer.