The problem here involves finding the perimeter of a shape created by cutting out a smaller semicircle from a larger semicircle.

Given Information:

1. Radius of the larger semicircle = $5 + 1 = 6$ cm.
2. Radius of the smaller semicircle = $5$ cm.
3. Value of $\pi$ = $3.14$.

Solution:

1. Calculate the circumference of the larger semicircle: $\text{Circumference of larger semicircle} = \pi \times \text{diameter} \times \frac{1}{2} = 3.14 \times (2 \times 6) \times \frac{1}{2} = 3.14 \times 6 = 18.84 \, \text{cm}$

2. Calculate the circumference of the smaller semicircle: $\text{Circumference of smaller semicircle} = \pi \times \text{diameter} \times \frac{1}{2} = 3.14 \times (2 \times 5) \times \frac{1}{2} = 3.14 \times 5 = 15.7 \, \text{cm}$

3. Calculate the perimeter of the shape:

   • The perimeter includes:
     • The arc of the larger semicircle $18.84$ cm,
     • The arc of the smaller semicircle $15.7$ cm,
     • The two straight-line segments (1 cm each) on either side.
   • Thus, the total perimeter is: $18.84 + 15.7 + 1 + 1 = 36.54 \, \text{cm}$

Final Answer:

The perimeter of the shape is 36.54 cm.

Would you like a deeper explanation or have any questions?

Related Questions:

1. How would the solution change if the radius of the smaller semicircle was 4 cm?
2. How is the perimeter affected if the distance between the semicircles is increased to 2 cm?
3. What is the area of the shaded region in the given figure?
4. Can you derive the general formula for the perimeter when the radii of the semicircles are given?
5. How would you calculate the total length of both arcs if the semicircles were complete circles?

Tip:

When dealing with semicircles, always remember to multiply the diameter by $\pi$ and then take half of it to find the arc length.