Pregunta
Question The diameter of a circle is 6 m . Find its area in terms of \( \pi \).
Ask by Pierce Martinez. in the United States
Mar 10,2025
Solución de inteligencia artificial de Upstudy
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The area of the circle is \( 9\pi \) square meters.
Solución
1. The radius \( r \) of the circle is half the diameter:
\[
r = \frac{6}{2} = 3 \text{ m}
\]
2. The area \( A \) of a circle is given by:
\[
A = \pi r^2
\]
3. Substitute the radius into the formula:
\[
A = \pi (3)^2 = 9\pi \text{ m}^2
\]
Thus, the area of the circle in terms of \( \pi \) is \( 9\pi \) m\(^2\).
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Simplifique esta solución The Deep Dive
The area \( A \) of a circle can be calculated using the formula \( A = \pi r^2 \), where \( r \) is the radius. Given the diameter is 6 m, the radius \( r \) is half of that, which is 3 m. Plugging this value into the area formula, we get \( A = \pi (3)^2 = 9\pi \) square meters. To visualize, think of a cozy pizza with a diameter of 6 meters—now imagine cutting it in half to figure out how much deliciousness fits within the circle's bounds. You’re left with an area of \( 9\pi \) m², which is quite a hearty slice of pizza pie!
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