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Areas Related to a Circle — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsAreas Related to a Circle1 Mark
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 $(b).$

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