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Step-1

Title: Arc length of sector

Grade: 7-a Lesson: S1-L7

Explanation:

Step	Type	Explanation	Answer
1	Problem	If the radius of a sector is 7m and \$\theta = 180^0\$. Find the arc length?
2	Formula:	Arc length of a sector.	l = \$\frac{\theta}{360^\circ} \times 2 \times \pi r\$
3	Step	Substitute \$22/7\$ for \$pi\$, \$180^\circ\$ for \$\theta\$ and 7 for r.	l = \$\frac{180°}{360°} \times 2 \times \frac{22}{7} \times 7\$
4	Step	Cancel out common factor.	\$l = \frac{\cancel{180°}}{\cancel{360°}} \times 2 \times \frac{22}{\cancel{7}^1} \times \cancel{7}^1 \$
5	Step	Cancel out common factor.	\$l = \frac{1}{\cancel{2}^1} \times \cancel{2}^1 \times \frac{22}{1} \times 1 \$
6	Step	Multiply.	\$ l = 22 \$
7		Answer	The arc length is \$22 m\$.

Step

Type

Explanation

Answer

Problem

If the radius of a sector is 7m and \$\theta = 180^0\$. Find the arc length?

Formula:

Arc length of a sector.

l = \$\frac{\theta}{360^\circ} \times 2 \times \pi r\$

Step

Substitute \$22/7\$ for \$pi\$, \$180^\circ\$ for \$\theta\$ and 7 for r.

l = \$\frac{180°}{360°} \times 2 \times \frac{22}{7} \times 7\$

Step

Cancel out common factor.

\$l = \frac{\cancel{180°}}{\cancel{360°}} \times 2 \times \frac{22}{\cancel{7}^1} \times \cancel{7}^1 \$

Step

Cancel out common factor.

\$l = \frac{1}{\cancel{2}^1} \times \cancel{2}^1 \times \frac{22}{1} \times 1 \$

Step

Multiply.

\$ l = 22 \$

Answer

The arc length is \$22 m\$.