question_answer

A bed of roses is like the figure given below. In the centre is a square and on each side there is a semi-circle. The side of the square is 21m. If each rose plant needs \[6\,\,{{\text{m}}^{2}}\] of space, then the number of plants in the bed is

A)  190 plants                    

B)  199 plants

C)  201 plants                    

D)  None of these

Correct Answer: D

Solution :

The side of square = 21 m \[\therefore \]Radius of each semi-circle = 105 m \[\therefore \]Area of semi-circle \[=4\left( \frac{1}{2}\pi {{r}^{2}} \right)\] \[=4\times \frac{1}{2}\times \frac{22}{7}\times 10.5\times 10.5=693\,\,{{m}^{2}}\] Area of square \[=21\times 21=441\,\,{{m}^{2}}\] \[\therefore \]Total area of bed \[=441+693=1134\,\,{{m}^{2}}\] As one rose plant needs \[6{{m}^{2}}\]space. \[\therefore \]Number of rose plant \[=\frac{\text{Total}\,\,\text{area}}{\text{Area}\,\,\text{required}\,\,\text{by}\,\,\text{one}\,\,\text{plant}}\] \[=\frac{1134}{6}=189\]plants