The circumference of a circular ground is 88 metres. A strip of land, 3 metres wide, inside and along the circumference of the ground is to be levelled. What is the budgeted expenditure if the levelling costs Rs. 7 per square metre ?

Solution(By Examveda Team)

Let the radius of the ground be R metres.
Then,
$$\eqalign{ & \Rightarrow 2\pi R = 88 \cr & \Rightarrow R = \left( {\frac{{88 \times 7}}{{2 \times 22}}} \right) \cr & \Rightarrow R = 14\,m \cr} $$
Area of land strip :
$$\eqalign{ & = \pi \left[ {{{\left( {14} \right)}^2} - {{\left( {11} \right)}^2}} \right]{m^2} \cr & = \left( {\frac{{22}}{7} \times 25 \times 3} \right){m^2} \cr & = \left( {\frac{{1650}}{7}} \right){m^2} \cr} $$
∴ Cost of levelling :
$$\eqalign{ & = {\text{Rs}}{\text{.}}\left( {\frac{{1650}}{7} \times 7} \right) \cr & = {\text{Rs}}{\text{. 1650}} \cr} $$