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\begin{tabular}{|l|l|}\hline 2. Eric needs to find the area of the base of a & 3. Wh \\ cylinder. Which formula should he use? & about \\ A. \( 2 \pi r \) & A. " \\ B. \( 2 \pi r h \) & B. " \\ C. \( \pi r^{2} \) & C. B \\ D. None of the above & D. \\ \hline\end{tabular}

Ask by Spencer Hodges. in the United States
Mar 17,2025

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Eric should use the formula \( \pi r^{2} \) to find the area of the base of the cylinder.

Solución

To find the area of the base of a cylinder, we need to identify the correct formula from the options provided. 1. **Understanding the problem**: The base of a cylinder is a circle. The area \( A \) of a circle is given by the formula: \[ A = \pi r^2 \] where \( r \) is the radius of the circle. 2. **Analyzing the options**: - **Option A**: \( 2 \pi r \) - This is the formula for the circumference of a circle, not the area. - **Option B**: \( 2 \pi r h \) - This is the formula for the surface area of a cylinder, not the area of the base. - **Option C**: \( \pi r^{2} \) - This is the correct formula for the area of the base of a cylinder. - **Option D**: None of the above - This is incorrect since option C is valid. 3. **Conclusion**: The correct formula Eric should use to find the area of the base of the cylinder is: \[ \pi r^{2} \] Thus, the answer is **C. \( \pi r^{2} \)**.

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Bonus Knowledge

To find the area of the base of a cylinder, Eric should use the formula for the area of a circle, which is \( \pi r^{2} \). This formula is derived from the fact that the base of a cylinder is a circular shape, where \( r \) is the radius. Remember, the area gives you the amount of space within the circle! When applying this formula, a common mistake is confusing the area with the circumference or volume. Ensure you use \( \pi r^{2} \) exclusively for area rather than mixing it up with formulas for other shapes or dimensions like \( 2 \pi r \) (which is the circumference) or \( 2 \pi r h \) (which represents the lateral surface area of the cylinder). Happy calculating!

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