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Lesson Example Discussion Quiz: Class Homework

Step-2

Title: Area of sector

Grade: 7-a Lesson: S1-L6

Explanation:

Step	Type	Explanation	Answer
1	Problem	If the radius of a sector is 35cm and \$\theta = 30^0\$. 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\$, \$30^\circ\$ for \$\theta\$ and 35 for r.	\begin{align} A &= \frac{30°}{360°} \times \frac{22}{7} \times 35^2 \\ \\ A &= \frac{30°}{360°} \times \frac{22}{7} \times 35 \times 35 \\ \end{align}
4	Step	Cancel out common factor.	\$A = \frac{\cancel{30°} ^{1} }{\cancel{360°} ^{12} } \times \frac{22}{\cancel{7}} \times \cancel{35} \times 35 \$
5	Step	Cancel out common factor.	\$ A &= \frac{1}{6} \times \frac{11}{1} \times 5 \times 35 \$
6	Step	Multiply.	\$A = \frac{1925}{6} \$
7	Step	Divide.	\$A = 320.84\$
8		Answer	The area is \$320.84 cm^2\$.

Step

Type

Explanation

Answer

Problem

If the radius of a sector is 35cm and \$\theta = 30^0\$. Find the area?

Formula:

Area of a sector.

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

Step

Substitute \$22/7\$ for \$pi\$, \$30^\circ\$ for \$\theta\$ and 35 for r.

\begin{align} A &= \frac{30°}{360°} \times \frac{22}{7} \times 35^2 \\ \\ A &= \frac{30°}{360°} \times \frac{22}{7} \times 35 \times 35 \\ \end{align}

Step

Cancel out common factor.

\$A = \frac{\cancel{30°} ^{1} }{\cancel{360°} ^{12} } \times \frac{22}{\cancel{7}} \times \cancel{35} \times 35 \$

Step

Cancel out common factor.

\$ A &= \frac{1}{6} \times \frac{11}{1} \times 5 \times 35 \$

Step

Multiply.

\$A = \frac{1925}{6} \$

Step

Divide.

\$A = 320.84\$

Answer

The area is \$320.84 cm^2\$.