The Canadian $2 coin has a copper centre surrounded by a ring of nickel. The diameter of the coin is 2.8 cm. The area of the copper centre is 2.0 cm2. What is the area of the nickel ring?
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To find the area of the nickel ring, we need to subtract the area of the copper centre from the total area of the coin.
The total area of the coin is the area of the entire circle, which can be calculated using the formula for the area of a circle:
A = π * r^2
Given that the diameter of the coin is 2.8 cm, we can calculate the radius (r) by dividing the diameter by 2:
r = 2.8 cm / 2 = 1.4 cm
Now, we can find the total area (A_total) of the coin:
A_total = π * (1.4 cm)^2
Next, we need to find the area of the copper centre (A_copper), which is given as 2.0 cm².
Finally, we can find the area of the nickel ring (A_ring) by subtracting the area of the copper centre from the total area of the coin:
A_ring = A_total - A_copper
Now, let's calculate the area of the nickel ring step-by-step:
Step 1: Calculate the radius of the coin
r = 2.8 cm / 2 = 1.4 cm
Step 2: Calculate the total area of the coin
A_total = π * (1.4 cm)^2
Step 3: Calculate the area of the copper centre
A_copper = 2.0 cm^2
Step 4: Calculate the area of the nickel ring
A_ring = A_total - A_copper
Substituting the values:
A_ring = (π * (1.4 cm)^2) - 2.0 cm²
Solving this equation will give us the area of the nickel ring.
To find the area of the nickel ring, we need to subtract the area of the copper center from the total area of the coin. Here's how you can calculate it:
1. First, find the radius of the coin:
- The diameter of the coin is given as 2.8 cm.
- Since the diameter is twice the radius, divide it by 2 to find the radius.
- Radius = 2.8 cm / 2 = 1.4 cm.
2. Next, calculate the area of the entire coin:
- The area of a circle is given by the formula: A = π * r^2, where A is the area and r is the radius.
- Substitute the given radius into the formula: A = π * (1.4 cm)^2.
- Calculate the area using the value of π (approximately 3.14159):
A = 3.14159 * (1.4 cm * 1.4 cm).
- Round the result to an appropriate number of decimal places if needed.
3. Finally, subtract the area of the copper center from the total area of the coin to get the area of the nickel ring:
- The area of the copper center is given as 2.0 cm^2.
- Subtract the area of the copper center from the total area of the coin obtained in step 2.
- Area of the nickel ring = Total area of the coin - Area of the copper center.
By following these steps, you should be able to find the area of the nickel ring on the Canadian $2 coin.