An ornamental circular lawn is surrounded by a path of uniform width

MATHEMATICS · Subjective · CBSE · Mathematics · Areas Related to Circles · Areas Related to Circles

Problem

An ornamental circular lawn is surrounded by a path of uniform width. The radius of the lawn is

r

metres and the width of the path is

w

metres. (a) Write an expression, in terms of

r

and

w

, for the area of the entire region (lawn plus path). (b) The area of the lawn alone is

616\pi\,\text{m}^2

and the area of the whole region is

900\pi\,\text{m}^2

. Form an equation in

w

and solve it to find the width of the path. (c) Using the value of

w

obtained in part (b), calculate the cost of paving the path at Rs.

150

per square metre.