Question

a fan blade on a ceiling fan makes one complete rotation in 25 seconds. blade is 16 inches long. how far will the tip of the fan blade travel in 40

160.9 inches

62.8 inches

2513.3 inches

1286.8 inches

Explanation:

Step1: Calculate the circumference of the circle traced by the fan - blade tip

The formula for the circumference of a circle is $C = 2\pi r$, where $r$ is the length of the fan - blade. Given $r = 16$ inches, so $C=2\pi\times16 = 32\pi$ inches.

Step2: Determine the number of rotations in 40 seconds

The fan makes 1 rotation in 25 seconds. Let the number of rotations in 40 seconds be $n$. Using the proportion $\frac{n}{40}=\frac{1}{25}$, we can solve for $n$: $n=\frac{40}{25}=\frac{8}{5}$ rotations.

Step3: Calculate the total distance traveled

The total distance $d$ traveled by the tip of the fan - blade is the number of rotations times the circumference of one rotation. So $d=n\times C=\frac{8}{5}\times32\pi$.
$d=\frac{256\pi}{5}\approx\frac{256\times3.14}{5}=\frac{803.84}{5}=160.768\approx160.9$ inches.

Answer:

160.9 inches