Question
11. The minute hand on a clock is 9 inches long. What is the area of the circle the minute hand covers after one hour?
Ask by Fowler Gordon. in the United States
Mar 20,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
El área del círculo que recorre la manecilla de los minutos es \( 81\pi \) pulgadas cuadradas.
Solution
1. Dado que la mano de los minutos actúa como el radio del círculo, se tiene que \( r = 9 \) pulgadas.
2. La fórmula para el área de un círculo es:
\[
A = \pi r^2
\]
3. Sustituimos \( r = 9 \) en la fórmula:
\[
A = \pi (9)^2 = \pi \times 81 = 81\pi
\]
4. Por lo tanto, el área del círculo que recorre la manecilla de los minutos es \( 81\pi \) pulgadas cuadradas.
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Simplify this solution Beyond the Answer
To find the area covered by the minute hand after one hour, you can treat the path as a circle. The radius of the circle is the length of the minute hand, which is 9 inches. The area (A) of a circle is calculated using the formula A = πr², where r is the radius. Plugging in the numbers: A = π(9)² = π(81) ≈ 254.47 square inches. So, the area the minute hand covers in one hour is about 254.47 square inches! Now, if you ever need to visualize this, just think about how the minute hand sweeps out that whole circle while ticking away the time! It’s like a giant pizza being sliced up at every tick, and yes, it’s an enormous pizza with an area of roughly 254.47 square inches! 🍕
