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Step-4

Title: Area of sector

Grade: 7-a Lesson: S1-L6

Explanation:

Step	Type	Explanation	Answer
1	Problem	The area of a sector is \$462cm^2 and \theta = 120^0\$. Find the radius?
2	Formula:	Area of a sector	A = \$\frac{\theta}{360^\circ} \times \pi r^2\$
3	Step	Substitute \$22/7\$ for \$pi\$ and \$120^\circ\$ for \$\theta\$ and 462 for A	462 = \$\frac{120°}{360°} \times \frac{22}{7} \times r^2\$
4	Step	Cancel out common factor	\$462 = \frac{\cancel{120°}}{\cancel{360°}} \times \frac{22}{7} \times r^2 \$
5	Step	Cancel out common factor	\$21 = \frac{1}{3} \times \frac{1}{7} \times r^2 \$
6	Step	Multiply.	\$21 = \frac{1}{3} \times \frac{1}{7} \times r^2 \$
7	Step	solve for r.	\$r = 21 \$
8		Answer	The radius is \$21 cm\$.

Step

Type

Explanation

Answer

Problem

The area of a sector is \$462cm^2 and \theta = 120^0\$. Find the radius?

Formula:

Area of a sector

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

Step

Substitute \$22/7\$ for \$pi\$ and \$120^\circ\$ for \$\theta\$ and 462 for A

462 = \$\frac{120°}{360°} \times \frac{22}{7} \times r^2\$

Step

Cancel out common factor

\$462 = \frac{\cancel{120°}}{\cancel{360°}} \times \frac{22}{7} \times r^2 \$

Step

Cancel out common factor

\$21 = \frac{1}{3} \times \frac{1}{7} \times r^2 \$

Step

Multiply.

\$21 = \frac{1}{3} \times \frac{1}{7} \times r^2 \$

Step

solve for r.

\$r = 21 \$

Answer

The radius is \$21 cm\$.