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Step-5

Title: Perimeter of semicircle

Grade: 7-a Lesson: S1-L5

Explanation:

Step	Type	Explanation	Answer
1	Problem	The perimeter of a semicircle is 108cm. Find the radius.
2	Formula:	Perimeter of a semicircle.	\$P = \pi r + d\$ \$p = \pi r + 2r\$ \$p = (\pi + 2)r\$
3	Step	Substitute \frac{22}{7} for \$pi\$ and 108 for P.	\$108 = (\frac{22}{7} + 2) \times r\$
4	Step	Multiply.	\$108 = \frac{36}{7} \times r\$
5	Step	Cancel out common factor.	\$\cancel(108)^3 = (\frac\cancel{36^1}{7}) \times r\$
6	Step	Multiply.	\$r = 21\$
7		Answer	The radius is \$21 cm\$.

Step

Type

Explanation

Answer

Problem

The perimeter of a semicircle is 108cm. Find the radius.

Formula:

Perimeter of a semicircle.

\$P = \pi r + d\$
\$p = \pi r + 2r\$
\$p = (\pi + 2)r\$

Step

Substitute \frac{22}{7} for \$pi\$ and 108 for P.

\$108 = (\frac{22}{7} + 2) \times r\$

Step

Multiply.

\$108 = \frac{36}{7} \times r\$

Step

Cancel out common factor.

\$\cancel(108)^3 = (\frac\cancel{36^1}{7}) \times r\$

Step

Multiply.

\$r = 21\$

Answer

The radius is \$21 cm\$.