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

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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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