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In one particular model of this bicycle, the diameter of the front wheel is    8/3 times the diameter of the rear wheel.9)For this model of bicycle, the ratio of the radius of the rear wheel to the radius of the front wheel is ___*1 point8:33:816:33:1610) When the bicycle travels 264 m, the rear wheel rotates 200 times. How many times does the front wheel rotate when the bicycle travels 264 m?*1 point7515020030011) Using the information in Question 2, calculate the diameter (in cm) of the front wheel of the bicycle. [Take π =22/7  ]*1 point5.6cm1.12cm56 cm112cm12) If there are 60 spokes in the front wheel of the bicycle. The angle between two consecutive spokes will be ___________*1 point1060636

Question

In one particular model of this bicycle, the diameter of the front wheel is    8/3 times the diameter of the rear wheel.9)For this model of bicycle, the ratio of the radius of the rear wheel to the radius of the front wheel is ___*1 point8:33:816:33:1610) When the bicycle travels 264 m, the rear wheel rotates 200 times. How many times does the front wheel rotate when the bicycle travels 264 m?*1 point7515020030011) Using the information in Question 2, calculate the diameter (in cm) of the front wheel of the bicycle. [Take π =22/7  ]*1 point5.6cm1.12cm56 cm112cm12) If there are 60 spokes in the front wheel of the bicycle. The angle between two consecutive spokes will be ___________*1 point1060636

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Solution

  1. The ratio of the radius of the rear wheel to the radius of the front wheel is 3:8. This is because the radius is half of the diameter, so if the diameter of the front wheel is 8/3 times the diameter of the rear wheel, the radius of the front wheel is also 8/3 times the radius of the rear wheel.

  2. The number of rotations of a wheel is inversely proportional to its diameter. Since the diameter of the front wheel is 8/3 times the diameter of the rear wheel, the front wheel will rotate 3/8 times as many times as the rear wheel for the same distance traveled. Therefore, if the rear wheel rotates 200 times when the bicycle travels 264 m, the front wheel will rotate 200 * (3/8) = 75 times.

  3. The distance a wheel travels in one rotation is equal to its circumference, which is π times its diameter. Therefore, if the rear wheel rotates 200 times to travel 264 m, the circumference of the rear wheel is 264 m / 200 = 1.32 m. Since the diameter is the circumference divided by π, the diameter of the rear wheel is 1.32 m / (22/7) = 0.42 m = 42 cm. Since the diameter of the front wheel is 8/3 times the diameter of the rear wheel, the diameter of the front wheel is 42 cm * (8/3) = 112 cm.

  4. The angle between two consecutive spokes in a wheel is equal to 360 degrees divided by the number of spokes. Therefore, if there are 60 spokes in the front wheel of the bicycle, the angle between two consecutive spokes will be 360 degrees / 60 = 6 degrees.

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