Lena measures a circular magnet and calculates that it has an area of 3.14 square inches. What is the magnet's diameter?
Question
Lena measures a circular magnet and calculates that it has an area of 3.14 square inches. What is the magnet's diameter?
Solution
To find the diameter of the magnet, we first need to understand the relationship between the area of a circle and its diameter. The formula for the area of a circle is πr², where r is the radius of the circle.
Given that the area of the magnet is 3.14 square inches, we can set up the equation:
3.14 = πr²
To solve for r, we divide both sides of the equation by π:
r² = 3.14/π
Taking the square root of both sides gives us the radius:
r = √(3.14/π)
Once we have the radius, we can find the diameter by multiplying the radius by 2:
d = 2r
Substituting the value of r from above:
d = 2 * √(3.14/π)
This will give us the diameter of the magnet.
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