Question
circular pond is surrounded by a $2m$ wide circular path. If outer circumference of circular path is $44m,$ find the inner circumference of the circular path. Also find area of the path.
✓
Answer
Let $R$ and $r$ be the radius outer circle and inner circle, respectively.
It is given that, circumference of outer circle is $44m.$
$\therefore2\pi\text{R}=44$
$ [\because$ circumference of circle of circle $=2\pi\text{r}]$
$\Rightarrow2\times\frac{44}{2\times\frac{22}{7}}=\frac{7\times44}{2\times22}=7\text{m}$
Since, $r = (R - 2)m = (7 - 2)m = 5m$
$\therefore$ Area circumference of the circlar path $2\pi\text{r}=2\times\frac{22}{7}\times5=31.43\text{m}$ (approx.)
$\because$ Area of path $=$ Area of outer circle $-$ Area of inner circle $=\pi(\text{R}^2-r^2)$
$=\frac{22}{7}(7^2 - 5^2)=\frac{22}{7}\times24=75.43\text{m}^2$ (approx.)
It is given that, circumference of outer circle is $44m.$
$\therefore2\pi\text{R}=44$
$ [\because$ circumference of circle of circle $=2\pi\text{r}]$
$\Rightarrow2\times\frac{44}{2\times\frac{22}{7}}=\frac{7\times44}{2\times22}=7\text{m}$
Since, $r = (R - 2)m = (7 - 2)m = 5m$
$\therefore$ Area circumference of the circlar path $2\pi\text{r}=2\times\frac{22}{7}\times5=31.43\text{m}$ (approx.)
$\because$ Area of path $=$ Area of outer circle $-$ Area of inner circle $=\pi(\text{R}^2-r^2)$
$=\frac{22}{7}(7^2 - 5^2)=\frac{22}{7}\times24=75.43\text{m}^2$ (approx.)
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