Semi-circle perimeter

Finding the perimeter of semi-circles using the formula $\large~P\,=\,\frac{\pi~d}{2}\,+\,d$.

 

What is the perimeter of a semi-circle with a diameter of 8cm?

To answer this question, we need to realize that the figure is just half of a circle. This means we will still be using the formula . However, there will be a twist in what we do, because the formula gives us the circumference of a complete circle.

You will solve this problem using three steps: find the circumference of a full circle with the same diameter, divide that circumference in half, and then add the diameter.

Example 1

What is the perimeter of a semi-circle with a diameter of 8cm?

Step 1: Find the circumference of the full circle.

Step 2: Divide the circumference in half.

This is the length of just the curvy part of the semi-circle.

Step 3: Add the diameter.

12.56 + 8 = 20.56 cm

This is the perimeter of the semi-circle!

 

 

Example 2

Find the perimeter of this quarter circle.

ex2

 

Example 3

A wire is bent to form three semicircles. Find the length of the wire in terms of .

ex3

 

 

Semi-circle circumference – CLASSWORK

 

Solve each of the following problems.

Find the perimeter of this shape.

 

Find the perimeter of this shape.

 


 

Self-Check


Question 1

 

A rope is arranged to form two semi-circles as shown. Find the length of the rope in terms of π.

 

 

[show answer]


Question 2

A garden is in the shape of a quarter circle. Find its perimeter. 

 

 

[show answer]


Question 3

A circle is drawn inside a square. Find the circumference of the circle. 

 

[show answer]


 

 

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