Question

The area of a circular path of uniform width h surrounding a circular region of radius r is

(a) $\mathrm{\pi }(2\mathrm{r}+\mathrm{h})\mathrm{r}$

(b) $\mathrm{\pi }(2\mathrm{r}+\mathrm{h})h$

(c) $\mathrm{\pi }(\mathrm{h}+\mathrm{r})\mathrm{r}$

(d) $\mathrm{\pi }(\mathrm{h}+\mathrm{r})h$

Answer 1

We have

Therefore, radius of the outer circle will be.

Now we will find the area between the two circles.

Cancelling we get,

Therefore, area of the circle is.

Hence, the correct answer is option (b).