question_answer

A circular lawn has an area of 1386 sq. metre. A path width 14 metre surrounds the lawn. What is the area of the lawn including the path? (in sq. metre)

A)  3850

B)  3560

C)  4820

D)  3250

E)  3920

Correct Answer: A

Solution :

                    Area of circular lawn = 1386 sq. metre \[\Rightarrow \text{ }\pi {{r}^{2}}=1386\] \[\Rightarrow \text{ }\frac{22}{7}\times {{r}^{2}}=1386\] \[\Rightarrow \text{ }{{\text{r}}^{2}}=\frac{1386\times 7}{22}=63\times 7\] \[\Rightarrow \text{ r=}\sqrt{63\times 7}=\sqrt{9\times 7\times 7}=21\,\,metre\] \[\therefore \] Radius of park with path \[=21+14=35\]metre \[\therefore \] Required area \[=\pi {{R}^{2}}\] \[=\frac{22}{7}\times 35\times 35\] = 3850 sq. metre