Questions: (09) What is the distance traveled, if a bicycle wheel, whose radius is 1.25 feet, makes 10 revolutions and a third of a revolution?

Solution Steps

To find the distance traveled by the bicycle wheel, we need to calculate the circumference of the wheel and then multiply it by the total number of revolutions. The circumference of a circle is given by \(2 \pi r\), where \(r\) is the radius. The total number of revolutions is 10 + 1/3.

The circumference \(C\) of a wheel is given by the formula: \[ C = 2 \pi r \] where \( r \) is the radius of the wheel. Given \( r = 1.25 \) feet, we have: \[ C = 2 \pi \times 1.25 \approx 7.854 \text{ feet} \]

The total number of revolutions is given as 10 and a third of a revolution: \[ \text{Total Revolutions} = 10 + \frac{1}{3} \approx 10.3333 \]

The distance traveled \(D\) is the product of the circumference and the total number of revolutions: \[ D = C \times \text{Total Revolutions} \] Substituting the values, we get: \[ D = 7.854 \times 10.3333 \approx 81.1578 \text{ feet} \]

Final Answer