Question

In the adjacent fig., OAPB is a sector of a circle of radius 3.5 cm centre at O and angle AOB = 120 degree. Find the length of OAPBO.

Answer 1

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Area of sector AOBP = 120×πr^2/360
= 120×22/7×3.5×3.5/360
=12.83cm^2

Area of sector AOBP = 1/2 × r × l
l = length oh an Arc APB.

12.83 = 1/2 × 3.5 × l
l = 12.83 × 2/3.5
l = 7.33


Perimeter of OAPBO = 2(radius) + l(length of arc)
=2(3.5)+7.33
=7 + 7.33
=14.33

length of OAPBO is 14.33cm.
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Answer 2

Length of the arc APB,

= $\sf{\frac{360 - 120}{360} \times 2\pi \: r}$

= $\sf{\frac{240}{360} \times 2 \times \frac{22}{7} \times 3.5cm}$

= $\sf{\frac{44}{3} cm}$

Hence, the length of OAPBO

= $\sf{OA+OB+arc\:APB}$

= $\sf{(3.5 + 3.5 + \frac{44}{3} )cm}$

= $\sf{(7 + \frac{44}{3} )cm}$

= ${\boxed{\sf{\frac{65}{3} cm}}}$