The image shows a problem involving two concentric circles, one inside the other. Here's a breakdown of the problem:

• Inner Circle: This circle has a radius of 2 inches.
• Outer Circle: This circle has a radius of 7 inches.
• Task: Determine the appropriate amounts of ribbon needed for each circle.

Let's solve this step by step:

1. Circumference of the Outer Circle:

   • The formula for the circumference $C$ of a circle is given by $C = 2\pi r$.
   • For the outer circle, $r = 7$ inches.
   • So, the circumference $C_{\text{outer}} = 2\pi \times 7 = 14\pi$ inches.

2. Circumference of the Inner Circle:

   • For the inner circle, $r = 2$ inches.
   • So, the circumference $C_{\text{inner}} = 2\pi \times 2 = 4\pi$ inches.

Now, let's fill in the blanks:

• Circumference of the larger circle: $14\pi$ inches.
• Circumference of the smaller circle: $4\pi$ inches.
• Total length of ribbon required:
  • Total ribbon length = $14\pi + 4\pi = 18\pi$ inches.
  • This equals approximately $18 \times 3.14 = 56.52$ inches.

Final Answers:

• Circumference of the larger circle: $14\pi$ inches or approximately 43.96 inches.
• Circumference of the smaller circle: $4\pi$ inches or approximately 12.56 inches.
• Total length of ribbon: 56.52 inches.

Would you like more details or have any questions?

Here are 5 related questions to consider:

1. How would the ribbon lengths change if the radius of the larger circle was increased by 1 inch?
2. What would be the area of the region between the two circles?
3. How can you find the diameter of each circle given only the circumference?
4. How does the circumference of a circle change if its radius is doubled?
5. What is the relationship between the circumference and the area of a circle?

Tip: Remember that the value of $\pi$ (pi) is approximately 3.14, but you can also use $\pi$ itself in calculations for more precise results, especially when dealing with symbolic or exact forms.