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Step-3

Title: Arc length of sector

Grade: 7-a Lesson: S1-L7

Explanation:

Step	Type	Explanation	Answer
1	Problem	If the radius of a 21m and \$\theta = 240^0\$. 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\$, \$240^\circ\$ for \$\theta\$ and 21 for r	l = \$\frac{240°}{360°} \times 2 \times \frac{22}{7} \times 21\$
4	Step	Cancel out common factor.	\$l = \frac{\cancel{240°} ^{2}}{\cancel{360°} ^{3}} \times 2 \times \frac{22}{\cancel{7}^1} \times \cancel{21}^3 \$
5	Step	Cancel out common factor.	\$l = \frac{2}{\cancel{3}^1} \times 2 \times \frac{22}{1} \times \cancel{3}^1 \$
6	Step	Multiply.	\$l = 88 \$
7		Answer	The arc length is \$88 m\$.

Step

Type

Explanation

Answer

Problem

If the radius of a 21m and \$\theta = 240^0\$. 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\$, \$240^\circ\$ for \$\theta\$ and 21 for r

l = \$\frac{240°}{360°} \times 2 \times \frac{22}{7} \times 21\$

Step

Cancel out common factor.

\$l = \frac{\cancel{240°} ^{2}}{\cancel{360°} ^{3}} \times 2 \times \frac{22}{\cancel{7}^1} \times \cancel{21}^3 \$

Step

Cancel out common factor.

\$l = \frac{2}{\cancel{3}^1} \times 2 \times \frac{22}{1} \times \cancel{3}^1 \$

Step

Multiply.

\$l = 88 \$

Answer

The arc length is \$88 m\$.