The radius of plate 1 is twice the radius of plate 2. The radius of plate 2 is 3 inches. What is the area of plate 1 in square inches?
Understand the Problem
The question is asking for the area of plate 1 based on its radius, which is defined in relation to the radius of plate 2. First, we need to find the radius of plate 1 and then use the formula for the area of a circle to calculate its area.
Answer
The area of plate 1 is \( 36\pi \) square inches.
Answer for screen readers
The area of plate 1 is ( 36\pi ) square inches, or approximately ( 113.04 ) square inches.
Steps to Solve
- Determine the radius of plate 1
Plate 1's radius is twice that of plate 2. Given that the radius of plate 2 is 3 inches, we calculate the radius of plate 1 as follows:
$$ \text{Radius of plate 1} = 2 \times \text{Radius of plate 2} = 2 \times 3 = 6 \text{ inches} $$
- Use the area formula for a circle
The formula to calculate the area ( A ) of a circle is:
$$ A = \pi r^2 $$
Where ( r ) is the radius of the circle. For plate 1, substitute ( r = 6 ) inches:
$$ A = \pi (6)^2 $$
- Calculate the area
Now calculate the area using the value of the radius:
$$ A = \pi \times 36 = 36\pi $$
- Approximate the area (if needed)
Using ( \pi \approx 3.14 ) for a numerical approximation:
$$ A \approx 36 \times 3.14 = 113.04 \text{ square inches} $$
The area of plate 1 is ( 36\pi ) square inches, or approximately ( 113.04 ) square inches.
More Information
The area of a circle increases with the square of the radius, meaning even a small increase in the radius results in a significant increase in area. The relationship between the sizes of plate 1 and plate 2 illustrates how scaling affects area.
Tips
- Misunderstanding radius relationships: Ensure to clearly identify the relationship between the radii of the two plates.
- Incorrect application of the area formula: Always double-check that the radius is used correctly in the formula.
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