question_answer

Circular footpath of width 2 m is constructed at the rate of Rs 20 per \[{{m}^{2}}\] around a circular park of radius 1500 m. Then, the total cost of construction of the footpath is [take, \[\pi =3.14\]]

A) Rs 37705.12

B) Rs 18852.56

C) Rs 377051.2

D) None of these

Correct Answer: C

Solution :

Radius of the park, i.e. inner radius of the park, r = 1500 m Width of the footpath around the park =2m Let R be the outer radius of the park including the footpath. Then,   A =(1500 + 2) m=1502 m Now, area of the footpath \[=\pi {{R}^{2}}-\pi {{r}^{2}}\] \[=\pi \left\{ {{R}^{2}}-{{r}^{2}} \right\}\] \[=3.14\left\{ {{\left( 1502 \right)}^{2}}-{{\left( 1500 \right)}^{2}} \right\}\] \[=3.14\left\{ \left( 1502+1500 \right)\left( 1502-1500 \right) \right\}\] \[=3.14\times 6004=18852.56{{m}^{2}}\] \[\therefore \] Total cost of construction of the footpath at the rate of Rs 20 per\[{{m}^{2}}\] \[=20\times 18852.56\] = Rs 377051.2