To find the area of the shaded annulus, we need to calculate the difference between the area of the large circle and the area of the small circle.

Given:

• Radius of the small circle ($r_1$) = 1.6 cm
• Radius of the large circle ($r_2$) = 6.3 cm

Steps to Calculate the Area

1. Area of the large circle ($A_{\text{large}}$): $A_{\text{large}} = \pi \times r_2^2 = \pi \times (6.3)^2$ $A_{\text{large}} = \pi \times 39.69$ $A_{\text{large}} \approx 124.56 \, \text{cm}^2$

2. Area of the small circle ($A_{\text{small}}$): $A_{\text{small}} = \pi \times r_1^2 = \pi \times (1.6)^2$ $A_{\text{small}} = \pi \times 2.56$ $A_{\text{small}} \approx 8.04 \, \text{cm}^2$

3. Area of the shaded annulus: $A_{\text{annulus}} = A_{\text{large}} - A_{\text{small}}$ $A_{\text{annulus}} \approx 124.56 - 8.04$ $A_{\text{annulus}} \approx 116.52 \, \text{cm}^2$

Answer:

The area of the shaded annulus is approximately 116.52 cm².

Would you like further details or have any questions?

Here are some related questions for further exploration:

1. How would the area change if the radius of the small circle increased by 1 cm?
2. What is the area of a circle with a radius of 10 cm?
3. How can you calculate the area of a semicircle with a given radius?
4. How would you find the circumference of both circles in this problem?
5. What would be the ratio of the areas of the large circle to the small circle?

Tip: When dealing with annulus areas, always remember to subtract the area of the inner circle from the outer circle to find the shaded region.