question_answer

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

A) \[\pi (2r+h)r\]

B) \[\pi (2r+h)h\]

C) \[\pi (h+r)r\]

D) \[\pi (h+r)h\]

Correct Answer: B

Solution :

[b] Here. radius of inner circle is r and width of path is h.

\[\therefore \] Radius of outer circle \[=r+h\]

Now, area of path

\[=\pi {{(r+h)}^{2}}-\pi {{r}^{2}}=\pi ({{r}^{2}}+{{h}^{2}}+2rh-{{r}^{2}})\]

\[=\pi (h+2r)h\]