Question
The difference between the circumference and radius of a circle is 37cm. Using $\pi=\frac{22}{7},$ find the circumference of the circle.
✓
Answer
Let r be the radius of a circle.
Then, circumference of a circle $=2\pi\text{r}$
We have,
Circumference - Radius = 37cm
$\Rightarrow2\pi\text{r}-\text{r}=37$
$\Rightarrow\text{r}(2\pi-1)=37$
$\Rightarrow\text{r}\Big(\frac{44}{7}-1\Big)=37$
$\Rightarrow\text{r}\Big(\frac{37}{7}\Big)=37$
$\Rightarrow\text{r}=\frac{37\times7}{37}$
$\Rightarrow\text{r}=7\text{cm}$
$\therefore$ Circumference of the circle $=2\pi\text{r}=\Big(2\times\frac{22}{7}\times7\Big)\text{cm}=44\text{cm}$
Then, circumference of a circle $=2\pi\text{r}$
We have,
Circumference - Radius = 37cm
$\Rightarrow2\pi\text{r}-\text{r}=37$
$\Rightarrow\text{r}(2\pi-1)=37$
$\Rightarrow\text{r}\Big(\frac{44}{7}-1\Big)=37$
$\Rightarrow\text{r}\Big(\frac{37}{7}\Big)=37$
$\Rightarrow\text{r}=\frac{37\times7}{37}$
$\Rightarrow\text{r}=7\text{cm}$
$\therefore$ Circumference of the circle $=2\pi\text{r}=\Big(2\times\frac{22}{7}\times7\Big)\text{cm}=44\text{cm}$
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