question_answer

A circular park is surrounded by a road 21 m wide. If the radius of the park is 105 m, then the area of the road is

A) \[1524.62\text{ }c{{m}^{2}}\]

B) \[15246\text{ }c{{m}^{2}}\]

C) \[15640.20\text{ }c{{m}^{2}}\]

D) None of these

Correct Answer: B

Solution :

Given that, a circular park is surrounded by a road. Width of the road = 21 m Radius of the park \[\left( {{r}_{i}} \right)=105\,m\] \[\therefore \]Radius of whole circular portion (park + road), \[{{r}_{e}}=105+21=126\,m\] Now, area of road = Area of whole circular portion — Area of Circular Park \[=\pi r_{e}^{2}-\pi r_{i}^{2}\]                    [\[\because \]area of circle = \[\pi {{r}^{2}}\]] \[=\pi \left( r_{e}^{2}-r_{i}^{2} \right)\] \[=\pi \,\left\{ {{\left( {{126}^{2}}-(105 \right)}^{2}} \right\}\] \[=\frac{22}{7}\times \left( 126+105 \right)\left( 126-105 \right)\] \[=\frac{22}{7}\times 231\times 21\] \[\left[ \because \,\,\left( {{a}^{2}}-{{b}^{2}} \right)=\left( a-b \right)\left( a+b \right) \right]\] \[=66\times 231=15246\,c{{m}^{2}}\] Hence, the required area of the road is \[15246\text{ }c{{m}^{2}}\].