A barrel shaped like a cylinder is laid on its side and rolled up a ramp. The barrel has a circular base that is 0.5 m in diameter. If the barrel turns 38 times in being rolled up the ramp, how long is the ramp? Use the value 3,14 for \( \pi \). Round your answer to the nearest tenth. Do not round any intermediate steps. m

To determine the length of the ramp, we can use the relationship between the number of rotations of the barrel and the distance it travels. 1. **Calculate the Circumference of the Barrel:** - The diameter of the barrel is \(0.5 \, \text{m}\), so the radius \(r\) is \(0.25 \, \text{m}\). - The circumference \(C\) of the barrel is given by: \[ C = \pi \times \text{diameter} = 3.14 \times 0.5 \, \text{m} = 1.57 \, \text{m} \] 2. **Determine the Total Distance Rolled:** - For each full rotation, the barrel travels a distance equal to its circumference. - Therefore, for \(38\) rotations, the total distance \(D\) is: \[ D = 38 \times C = 38 \times 1.57 \, \text{m} = 59.66 \, \text{m} \] 3. **Round the Answer:** - Rounding \(59.66 \, \text{m}\) to the nearest tenth gives: \[ D \approx 59.7 \, \text{m} \] **Final Answer:** The ramp is approximately **59.7 m** long.