A sector is formed by a circular arc with a radius of 9 cm, subtending an 18° angle at the centre. What is its perimeter? (Use π = 3.14) (Rounded up to two decimal places.)

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The correct option is 20.83 cm.

Step-by-Step Explanation:

1. Understand the components of a sector's perimeter:
A sector of a circle is bounded by two radii and an arc. Therefore, the total perimeter of the sector includes the length of the circular arc plus the lengths of the two bounding radii.

$\text{Perimeter of Sector}=\text{Arc Length}+2\times \text{Radius}$

2. Calculate the arc length:
Given:
Radius ($r$) = 9 cm
Central angle ($\theta$) = 18°
Value of $\pi$ = 3.14

The formula for the length of a circular arc is:

$\text{Arc Length}=\frac{\theta }{360°}\times 2\pi r$

Substitute the given values into the formula:

$\text{Arc Length}=\frac{18}{360}\times 2\times 3.14\times 9$

$\text{Arc Length}=\frac{1}{20}\times 56.52$

$\text{Arc Length}=0.05\times 56.52=2.826\text{cm}$

3. Calculate the total perimeter of the sector:

$\text{Perimeter}=2.826\text{cm}+2\times 9\text{cm}$

$\text{Perimeter}=2.826\text{cm}+18\text{cm}=20.826\text{cm}$

4. Round to two decimal places:
Rounding 20.826 cm up to two decimal places gives 20.83 cm.