MCQ
If the difference between the circumference and radius of a circle is $37\ cm,$ then using $\pi=\frac{22}{7}$ the circumference $($in $cm)$ of the circle is:
- A$154$
- ✓$44$
- C$14$
- D$7$
✓
Answer
Correct option: B.
$44$
We know that circumference;
$C$ of the circle with radius $r$ is equal to $2\pi\text{r}$
We have given difference between circumference and radius of the citcle that is $37\ cm,$
$\therefore\text{C}-\text{r}=2\pi\text{r}-\text{r}$
$\therefore(2\pi-1)\text{r}=37$
Substituting we $\pi=\frac{22}{7}$ get,
$\therefore\Big(2\times\frac{22}{7}-1\Big)\text{r}=37$
$\therefore\Big(\frac{44-7}{7}\Big)\text{r}=37$
$\therefore\Big(\frac{37}{7}\Big)\text{r}=37$
Dividing both sides of the equation by $\frac{7}{37},$ we get,
$\therefore\text{r}=7$
Threfore, circumference of the circle will be
$2\pi\text{r}=2\times\frac{22}{7}\times7$
$=44\text{cm}^2$
Hence, the correct choice is $(b).$
$C$ of the circle with radius $r$ is equal to $2\pi\text{r}$
We have given difference between circumference and radius of the citcle that is $37\ cm,$
$\therefore\text{C}-\text{r}=2\pi\text{r}-\text{r}$
$\therefore(2\pi-1)\text{r}=37$
Substituting we $\pi=\frac{22}{7}$ get,
$\therefore\Big(2\times\frac{22}{7}-1\Big)\text{r}=37$
$\therefore\Big(\frac{44-7}{7}\Big)\text{r}=37$
$\therefore\Big(\frac{37}{7}\Big)\text{r}=37$
Dividing both sides of the equation by $\frac{7}{37},$ we get,
$\therefore\text{r}=7$
Threfore, circumference of the circle will be
$2\pi\text{r}=2\times\frac{22}{7}\times7$
$=44\text{cm}^2$
Hence, the correct choice is $(b).$
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