| The external fencing of a circular path around a circular plot of land is 33 m more than its interior fencing. The width of the path around the plot is |
A) 5.52 m
B) 5.25 m
C) 2.55 m
D) 2.25 m
Correct Answer: B
Solution :
| Let interior circumference of circular path \[=x\,\,m\]and external circumference of circular path\[=(x+33)\,\,m\] |
| Now, let internal radius \[={{r}_{1}}\] |
| and external radius \[={{r}_{2}}\] |
| \[\therefore \]\[x=2\pi {{r}_{1}}\]and \[(x+33)=2\pi {{r}_{2}}\] |
| On subtracting these, we get |
| \[33=2\pi \,\,({{r}_{2}}-{{r}_{1}})\] |
| \[\Rightarrow \]\[{{r}_{2}}-{{r}_{1}}=\frac{33}{2\pi }=\frac{33\times 7}{2\times 22}=\frac{21}{4}=5.25\,\,m\] |
| Hence, the width of the path \[={{r}_{2}}-{{r}_{1}}\,\,\,\,5.25\,\,m\] |
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