Question

If the length of the major arc formed when the radii subtend an angle of $120$ degree at the center is $150cm$, find the circumference of the circle.

• A. $450cm$
• B. $180cm$
• C. $225cm$
• D. None of the above

Answer 1

The correct option is C $225cm$


Angle subtended at the center by the radii of the cirlce $=120$ degree

When we consider the major arc $AB$ formed,

the angle at the center $\theta =360-120=240$ degree
Length of the arc $AB=150cm$
$⟹150=\frac{\theta }{360}\times \pi \times d$

$⟹150=\frac{240}{360}\times \pi \times d$

$⟹150=\frac{2}{3}\times \pi \times d$

$⟹150\times \frac{3}{2}=\pi \times d$

$⟹75\times 3=\pi \times d$

$⟹225=\pi \times d$, which is the circumference of the circle.

Therefore, the circumference of the circle $=225cm$

Option (c.) is correct.