To find the area of the shaded region between the two circles, we follow these steps:

Step 1: Find the radii of the two circles

• The inner circle's diameter $d = 8 \, \text{cm}$, so its radius $r_{\text{inner}}$ is: $r_{\text{inner}} = \frac{d}{2} = \frac{8}{2} = 4 \, \text{cm}.$
• The outer circle's radius $r_{\text{outer}}$ is given as $6 \, \text{cm}$.

Step 2: Calculate the areas of the two circles

The formula for the area of a circle is: $\text{Area} = \pi r^2.$ Using $\pi \approx 3.14$:

1. Area of the outer circle: $\text{Area}_{\text{outer}} = 3.14 \times (6)^2 = 3.14 \times 36 = 113.04 \, \text{cm}^2.$

2. Area of the inner circle: $\text{Area}_{\text{inner}} = 3.14 \times (4)^2 = 3.14 \times 16 = 50.24 \, \text{cm}^2.$

Step 3: Find the area of the shaded region

The shaded region is the area of the outer circle minus the area of the inner circle: $\text{Area}_{\text{shaded}} = \text{Area}_{\text{outer}} - \text{Area}_{\text{inner}}.$ Substitute the values: $\text{Area}_{\text{shaded}} = 113.04 - 50.24 = 62.8 \, \text{cm}^2.$

Final Answer:

The area of the shaded region is: $\boxed{62.8 \, \text{square centimeters}}$

Let me know if you need further clarification or another example! 😊

Related Questions:

1. How do you find the area of a sector of a circle?
2. What is the circumference of the outer circle in this problem?
3. How would the shaded area change if the outer radius was doubled?
4. If the inner circle had a different radius, how would you approach this problem?
5. What is the formula for calculating the area difference between two concentric circles?

Tip: Always double-check radii or diameters when solving for circular areas. Converting between them is key!