LESSON E/ SESEION 3 (3) The diameter of a Canadian penny is 19 millimeters. The diameter of a Ganadian nicket is 27 mimimeters. How moch greater is the area of a Canadian inckat than the area of a Eanatian penny? show your work.

Sure, let's solve the problem step by step. **Problem Statement:** - The diameter of a Canadian penny is **19 millimeters**. - The diameter of a Canadian nickel is **27 millimeters**. - **Question:** How much greater is the area of a Canadian nickel than the area of a Canadian penny? **Solution:** 1. **Understand the Formula for the Area of a Circle:** The area \( A \) of a circle is given by the formula: \[ A = \pi r^2 \] where \( r \) is the radius of the circle. 2. **Calculate the Radius of Each Coin:** The radius is half of the diameter. - **Penny:** \[ \text{Diameter} = 19 \text{ mm} \\ \text{Radius} = \frac{19}{2} = 9.5 \text{ mm} \] - **Nickel:** \[ \text{Diameter} = 27 \text{ mm} \\ \text{Radius} = \frac{27}{2} = 13.5 \text{ mm} \] 3. **Calculate the Area of Each Coin:** - **Penny:** \[ A_{\text{penny}} = \pi \times (9.5)^2 = \pi \times 90.25 \approx 283.53 \text{ mm}^2 \] - **Nickel:** \[ A_{\text{nickel}} = \pi \times (13.5)^2 = \pi \times 182.25 \approx 572.56 \text{ mm}^2 \] 4. **Find the Difference in Areas:** \[ \text{Difference} = A_{\text{nickel}} - A_{\text{penny}} \\ \text{Difference} \approx 572.56 \text{ mm}^2 - 283.53 \text{ mm}^2 = 289.03 \text{ mm}^2 \] 5. **Conclusion:** The area of a Canadian nickel is approximately **289 square millimeters** greater than the area of a Canadian penny. **Final Answer:** The Canadian nickel has an area approximately 289 mm² greater than the Canadian penny.