Question

AnSwEr ThiS qUeStiOn (◍•ᴗ•◍)

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Answer 1

Given :

• OAPB is a sector of a circle of radius 3.5 cm with center 'O' .
• $\sf\angle\:AOB=120\degree$

To find :

• Length of OAPBO.

Solution :

$\sf\angle\:AOB(\theta)=120\degree$

Radius (r) = 3.5 cm.

$\sf{Now,\: length\:of\:Arc(\widehat{AB})=2\pi\:r\times\frac{\theta}{360\degree}}$

$\to\sf{Length\:of\:Arc(\widehat{AB})=2\times\frac{22}{7}\times\:3.5\times\frac{120}{360}\:cm}$

$\to\sf{Length\:of\:Arc(\widehat{AB})=7.3\:cm}$

Circumference of the circle = 2πr

→ Circumference = $\sf{2\times\frac{22}{7}\times\:3.5\:cm}$

→ Circumference = 22 cm.

Now,

$\sf{Length\:of\:Arc(\widehat{APB})=Circumference-Length\:of\:Arc\:AB}$

$\to\sf{Length\:of\:Arc(\widehat{APB})=(22-7.3)\:cm}$

$\to\sf{Length\:of\:Arc(\widehat{APB})=14.7\:cm}$

Therefore, the length of OAPBO is 14.7 cm.