Lesson Example Discussion Quiz: Class Homework |
Step-5 |
Title: Area of sector |
Grade: 7-a Lesson: S1-L6 |
Explanation: |
| Step | Type | Explanation | Answer |
|---|---|---|---|
1 |
Problem |
The area of a sector is 3080m^2 and radius is 84m. Find the \$\theta\$? |
|
2 |
Formula: |
Area of a sector. |
\$A = \frac{\theta}{360^\circ} \times \pi r^2\$ |
3 |
Step |
Substitute \$22/7\$ for \$pi\$, 84 for r and 3080 for A. |
\$3080 = \frac{\theta}{360°} \times \frac{22}{7} \times 84 \times 84\$ |
4 |
Step |
Cancel out common factor. |
\$3080 = \frac{\theta}{360°} \times \frac{22}{\cancel{7}^1} \times \cancel{84}^12 \times 84 \$ |
5 |
Step |
Cancel out common factor. |
\$3080 = \frac{\theta}{\cancel{360°}} \times \frac{22}{1} \times \cancel{12}^1 \times 84 \$ |
6 |
Step |
Cancel out common factor. |
\$\cancel{3080} ^{140} = \frac{\theta}{30°} \times \frac{\cancel{22}^1}{1} \times 1 \times 84 \$ |
7 |
Step |
Cancel out common factor. |
\$\cancel{140} ^{20} = \frac{\theta}{30°} \times \cancel{84} ^{12} \$ |
8 |
Step |
Cancel out common factor. |
\$\cancel{20} ^{10}= \frac{\theta}{30°} \times \cancel{12}^6 \$ |
9 |
Step |
Cancel out common factor. |
\$10 = \frac{\theta}{\cancel{30°}} \times \cancel{6}^1 \$ |
10 |
Step |
Multiply |
\$10 = \frac{\theta}{5°}\$ |
11 |
Step |
Solve for \$\theta\$. |
\$\theta = 50° \$ |
12 |
Answer |
The \$\theta\$ is \$50°\$. |
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