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Which of the following can be used to find the area of a circle? A. \( r \pi^{2} \) B. \( \pi d^{2} \) C. \( d \pi^{2} \) D. \( \pi r^{2} \)

Ask by Hobbs Cervantes. in the United States
Mar 12,2025

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Answer

The area of a circle is found using \( \pi r^{2} \).

Solution

To find the area of a circle, we can use the formula: \[ A = \pi r^{2} \] where \( A \) is the area and \( r \) is the radius of the circle. Now, let's analyze the options provided: A. \( r \pi^{2} \) - This is not the correct formula for the area of a circle. B. \( \pi d^{2} \) - This is also not correct. The correct formula using diameter \( d \) is \( \frac{\pi d^{2}}{4} \). C. \( d \pi^{2} \) - This is not the correct formula for the area of a circle. D. \( \pi r^{2} \) - This is the correct formula for the area of a circle. Thus, the correct answer is: **D. \( \pi r^{2} \)**.

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Extra Insights

To find the area of a circle, the most commonly used formula is \( \pi r^{2} \), where \( r \) is the radius. This formula stems from the geometry of circles, expressing how the area grows in relation to the radius squared. Just imagine covering the circle with little squares, and you'll see how those squares multiply based on the radius! In historical contexts, the formula for the area of a circle was first understood by ancient mathematicians such as Archimedes. By inscribing polygons within a circle and calculating their areas, he approximated the area of circles long before the formula was formally derived. Isn’t it fascinating how math has historical roots that connect us to the great thinkers of the past?

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