Lesson Example Discussion Quiz: Class Homework |
Step-3 |
Title: Perimeter of sector |
Grade: 7-a Lesson: S1-L8 |
Explanation: |
| Step | Type | Explanation | Answer |
|---|---|---|---|
1 |
Problem |
If the arc length of a sector is 352m and \$\theta = 320^0\$. Find the perimeter? |
|
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. |
\$352 &= \frac{\cancel{320°}}{\cancel{360°}} \times 2 \times \frac{22}{7} \times r \$ |
5 |
Step |
Cancel out common factor. |
\$\cancel{352} ^{32} = \frac{8}{9} \times 2 \times \frac{\cancel{22} ^{2} }{7} \times r \$ |
6 |
Step |
Cancel out common factor. |
\$\cancel{32}^4 = \frac{\cancel{8}^1}{9} \times 2 \times \frac{2}{7} \times r \$ |
7 |
Step |
Cancel out common factor. |
\$\cancel{4}^2 = \frac{1}{9} \times \cancel{2}^1 \times \frac{2}{7} \times r \$ |
8 |
Step |
Cancel out common factor. |
\$\cancel{2}^1 = \frac{1}{9} \times 1 \times \frac{\cancel{2}^1}{7} \times r\$ |
9 |
Step |
Multiply. |
\$1 = \frac{1}{63} \times r \$ |
10 |
Step |
Solve for r. |
\$ r = 63 \$ |
11 |
Formula: |
Perimeter of a sector. |
\$P = 2r + l\$ |
12 |
Step |
Substitute 352 for l and 63 for r. |
\$ P = 2(63) + 352\$ |
13 |
Step |
Multiply. |
\$ P = 126 + 352\$ |
14 |
Step |
Add. |
\$ P = 488 \$ |
15 |
Answer |
The perimeter is \$478 m\$. |
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