Respuesta :
The circumference of a circle of radius r is given by:
[tex]C=2\pi r[/tex]This represents the length rolled by the circle when it makes one full rotation. If it makes an angle of θ radians, the length is:
[tex]L=\theta r[/tex]a) It's required to calculate the length rolled by the bicycle when it rotates 90 degrees. We need to convert degrees to radians as follows:
[tex]\theta=90\cdot\frac{\pi}{180}=\frac{\pi}{2}[/tex]The radius of the bicycle is half the diameter:
r = 2 feet / 2 = 1 feet.
Calculate L:
[tex]\begin{gathered} L=\frac{\pi}{2}\cdot1\text{ feet} \\ L=\frac{\pi}{2}\text{ feet} \end{gathered}[/tex]The question does not specify the format of the answer, so we also provide an approximate answer below:
L ≈ 3.14 / 2 = 1.57 feet
b) The length of one rotation is:
[tex]\begin{gathered} C=2\pi(1\text{ foot}) \\ C=2\pi\text{ feet} \end{gathered}[/tex]For 1'0 rotations:
[tex]\begin{gathered} C=10\cdot2\pi\text{ feet} \\ C=20\pi\text{ feet} \end{gathered}[/tex]Approximating C ≈ 20 x 3.14 = 62.8 feet
