MCQ
If the difference between the circumference and radius of a circle is $37\ cm$, then its area is:
- ✓$154\ cm^2$
- B$160\ cm^2$
- C$200\ cm^2$
- D$150\ cm^2$
✓
Answer
Correct option: A.
$154\ cm^2$
Let $r$ be the radius of a circle then circum$-$ference $=2\pi\text{r}$
$\therefore2\pi\text{ r}-\text{r}=37$
$\text{r}\Big(2\times\frac{22}{7}-1\Big)=37$
$\Rightarrow\text{r}\Big(\frac{44}{7}-7\Big)=37$
$\Rightarrow\text{r}\Big(\frac{37}{7}\Big)=37$
$\Rightarrow\text{r}=\frac{37\times7}{37}$
$=7\ \text{cm}$
Now area of the circle $=\pi\text{r}^2$
$=\frac{22}{7}\times7\times7$
$=154\ \text{cm}^2\text{(a)}$
$\therefore2\pi\text{ r}-\text{r}=37$
$\text{r}\Big(2\times\frac{22}{7}-1\Big)=37$
$\Rightarrow\text{r}\Big(\frac{44}{7}-7\Big)=37$
$\Rightarrow\text{r}\Big(\frac{37}{7}\Big)=37$
$\Rightarrow\text{r}=\frac{37\times7}{37}$
$=7\ \text{cm}$
Now area of the circle $=\pi\text{r}^2$
$=\frac{22}{7}\times7\times7$
$=154\ \text{cm}^2\text{(a)}$
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