question_answer 29)

A circular flower bed is surrounded by \[\alpha \] path 4 m wide. The diameter of the flower bed is 66 m. What is the area of this path? \[(\text{Take}\pi =\text{3}.\text{14})\]

Answer:

                Diameter of the flower bed\[=\text{66 m}\]                     \[\Rightarrow \]               Radius of the flower bed (r) \[\text{= }\frac{\text{66}}{\text{2}}\text{m = 33 m}\] \[\therefore \]                  Area of the flower bed  \[=\pi {{r}^{2}}\] \[\text{= 3}\text{.14  }\!\!\times\!\!\text{  (33}{{\text{)}}^{\text{2}}}\text{ }{{\text{m}}^{\text{2}}}\] \[\text{= 3}\text{.14  }\!\!\times\!\!\text{  1089 }{{\text{m}}^{\text{2}}}\text{ = 3419}\text{.46 }{{\text{m}}^{\text{2}}}\] Radius of the flower bed with path (R) \[=\text{33 m}+\text{4 m}=\text{37 m}\] \[\therefore \] Area of the flower bed with path \[=\pi {{R}^{2}}\] \[=\text{3}.\text{14}\times {{(\text{37})}^{\text{2}}}{{\text{m}}^{\text{2}}}=\text{3}.\text{14}\times \text{1369 }{{\text{m}}^{\text{2}}}\] \[=\text{4298}.\text{66 }{{\text{m}}^{\text{2}}}\] \[\therefore \]                  Area of the path = Area of the flower bed with path - Area of the flower bed \[=\text{4298}.\text{66 }{{\text{m}}^{\text{2}}}-\text{3419}.\text{46 }{{\text{m}}^{\text{2}}}\]                 \[\text{= 879}\text{.20 }{{\text{m}}^{\text{2}}}\]