Question

The circular wire of diameter $10$cm is cut and placed along the circumference of a circle of diameter $1$ m. The angle subtended by the wire at the centre of the circle is equal to:

• A. $\frac{\pi }{4}$
• B. $\frac{\pi }{3}$
• C. $\frac{\pi }{5}$
• D. $\frac{\pi }{10}$

Answer 1

The correct option is C $\frac{\pi }{5}$

Perimeter of smaller circle$=2\pi r$

$=2\pi \times 10=20\pi ㎝$

(Image)

Circumference of Arc AOB$=2\pi R\times \frac{x°}{360°}$

$2\pi \times 1m\times \frac{x°}{360°}=20\pi ㎝$

$200\pi \times \frac{x°}{360°}=2\pi$

$\frac{x}{360}=\frac{1}{10}$

$x=36°=\frac{\pi }{5}$