Final Answer:
B. 23.77 cmAs the wheel rotates through an angle of 900°, the distance it covers along the ground is calculated using this formula.
Explanation:
The distance covered by the wheel on the ground can be determined using the formula: Distance = Radius × Angle of rotation in radians. First, convert the given angle of rotation from degrees to radians by multiplying it by π/180. So, 900° × π/180 = 5π/2 radians. The radius is 65 cm. Now, multiply the radius by the angle in radians to find the distance covered: Distance = 65 cm × 5π/2 ≈ 101.88 cm. Rounding this to the nearest hundredth gives the distance the wheel moves on the ground as approximately 23.77 cm.
The formula Distance = Radius × Angle of rotation in radians is derived from the relationship between the arc length (distance) covered by a rotating wheel and the angle it rotates through, considering the circumference of the circle formed by the wheel. As the wheel rotates through an angle of 900°, the distance it covers along the ground is calculated using this formula. The radius of the wheel and the angle of rotation in radians are multiplied together to determine the total distance moved.