Final answer:
Malcolm's circle with a radius of 3 inches would have a diameter of 6 inches, calculated by multiplying the radius by 2.
Step-by-step explanation:
The student's question involves finding the diameter of a circle, given that the radius is 3 inches. In geometry, a fundamental relationship between the radius and the diameter of a circle is that the diameter is twice as long as the radius. Therefore, since the radius is given as 3 inches, the diameter can be found by multiplying the radius by 2.
Step-by-step calculation:
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- Start with the known radius of the circle, which is 3 inches.
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- Multiply the radius by 2 to find the diameter.
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- Since 3 inches multiplied by 2 equals 6 inches, the diameter of the circle is 6 inches.
Therefore, Malcolm's circle with a radius of 3 inches has a diameter of 6 inches. This approach to find the diameter using the given radius demonstrates a principle that has been understood for over two millennia, including by the ancient Greeks who recognized that the perimeter or circumference of a circle with radius r is 2πr, where the Greek letter π (pi) is a number approximately equal to 3.14159.