Question:
The difference between the circumference and radius of a circle is 37 cm. The area of the circle is
(a) 111 cm2
(b) 184 cm2
(c) 154 cm2
(d) 259 cm2
Solution:
(c) 154 cm2
Let the radius be r cm.
We know:
Circumference of the circle $=2 \pi \mathrm{r}$
Thus, we have:
$2 \pi r-r=37$
$\Rightarrow r(2 \pi-1)=37$
$\Rightarrow r\left(2 \times \frac{22}{7}-1\right)=37$
$\Rightarrow r\left(\frac{37}{7}\right)=37$
$\Rightarrow r=\left(37 \times \frac{7}{37}\right)$
$\Rightarrow r=7 \mathrm{~cm}$
Radius = 7 cm
Now,
Area of the circle $=\pi r^{2}$
$=\left(\frac{22}{7} \times 7 \times 7\right) \mathrm{cm}^{2}$
$=154 \mathrm{~cm}^{2}$
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