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Step-3

Title: Area of sector

Grade: 7-a Lesson: S1-L6

Explanation:

Step	Type	Explanation	Answer
1	Problem	If the radius of a sector is 14m \$\theta = 40^0\$. Find the area?
2	Formula:	Area of a sector.	A = \$\frac{\theta}{360^\circ} \times \pi r^2\$
3	Step	Substitute \$22/7\$ for \$pi\$, \$40^\circ\$ for \$\theta\$ and 14 for r.	A = \$\frac{40°}{360°} \times \frac{22}{7} \times 14^2\$
4	Step	Cancel out common factor.	\$A = \frac{\cancel{40°}}{\cancel{360°}} \times \frac{22}{\cancel{7}} \times \cancel{14} \times 14 \$
5	Step	Multiply.	\$ A = \frac{1}{9} \times \frac{22}{1} \times 2 \times 14 \$
6	Step	Divide.	\$ A = 68.45 \$
7		Answer	The area is \$68.45 m^2\$.

Step

Type

Explanation

Answer

Problem

If the radius of a sector is 14m \$\theta = 40^0\$. Find the area?

Formula:

Area of a sector.

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

Step

Substitute \$22/7\$ for \$pi\$, \$40^\circ\$ for \$\theta\$ and 14 for r.

A = \$\frac{40°}{360°} \times \frac{22}{7} \times 14^2\$

Step

Cancel out common factor.

\$A = \frac{\cancel{40°}}{\cancel{360°}} \times \frac{22}{\cancel{7}} \times \cancel{14} \times 14 \$

Step

Multiply.

\$ A = \frac{1}{9} \times \frac{22}{1} \times 2 \times 14 \$

Step

Divide.

\$ A = 68.45 \$

Answer

The area is \$68.45 m^2\$.