Question

The difference between the circumference and radius of a circle is 37 cm. The area of the circle is

(a) 111 cm²
(b) 148 cm²
(c) 154 cm²
(d) 259 cm²

Answer 1

(c) 154 cm²

Let the radius of the circle be r cm.
Circumference = $2\mathrm{\pi r}$

(Circumference) - (Radius) = 37
∴ $\left(2\mathrm{\pi r}-\mathrm{r}\right)=37$
⇒ $r\left(2\mathrm{\pi }-1\right)=37$
⇒ r = $\frac{37}{\left(2\mathrm{\pi }-1\right)}$ = $\frac{37}{\left(2\times {\displaystyle \frac{22}{7}}-1\right)}=\frac{37}{\left({\displaystyle \frac{44}{7}}-1\right)}=\frac{37}{\left({\displaystyle \frac{44-7}{7}}\right)}=\left(\frac{37\times 7}{37}\right)=7$
∴ Radius of the given circle is 7 cm.
∴ Area = ${\mathrm{\pi r}}^2$ = $\left(\frac{22}{7}\times 7\times 7\right)$ cm² = 154 cm²