A wheel makes 20 revolutions per hour. The radians turns through 25 minutes is __________.

Options

A. `(50pi^(c))/(7)`
B. `(250pi^(c))/(3)`
C. `(150pi^(c))/(7)`
D. `(50pi^(c))/(3)`

Explanation

To find the radians turned through by a wheel that makes 20 revolutions per hour in 25 minutes, we can follow these steps:

### Step 1: Calculate the number of revolutions in 25 minutes.
Given that the wheel makes 20 revolutions in 1 hour (which is 60 minutes), we can find the number of revolutions in 1 minute:
\[ \text{Revolutions per minute} = \frac{20 \text{ revolutions}}{60 \text{ minutes}} = \frac{1}{3} \text{ revolutions per minute} \]

Now, to find the number of revolutions in 25 minutes:
\[ \text{Revolutions in 25 minutes} = \left(\frac{1}{3} \text{ revolutions per minute}\right) \times 25 \text{ minutes} = \frac{25}{3} \text{ revolutions} \]

### Step 2: Convert revolutions to radians.
We know that 1 revolution is equal to \(2\pi\) radians. Therefore, to find the total radians for \(\frac{25}{3}\) revolutions:
\[ \text{Radians} = \left(\frac{25}{3} \text{ revolutions}\right) \times (2\pi \text{ radians per revolution}) = \frac{25 \times 2\pi}{3} = \frac{50\pi}{3} \text{ radians} \]

### Final Answer:
The radians turned through in 25 minutes is \(\frac{50\pi}{3}\).

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