If a wheel rolls a distance of 75 inches as it turns through an angle of 200. the radius of the wheel would be 2.6 inches.
[tex]2\pi^c = 360^\circ = \text[/tex] {Full circumference}
The superscript 'c' shows the angle measured is in radians.
If the radius of the circle is of r units, then:
[tex]1^c \: \rm covers \: \dfrac{circumference}{2\pi} = \dfrac{2\pi r}{2\pi} = r\\\\or\\\\\theta^c \: covers \:\:\: r \times \theta \: \rm \text{units of arc}[/tex]
we have given a wheel rolls a distance of 75 inches as it turns through an angle of 200.
we know that
arc = angle x radius
radius = arc/ angle
[tex]\dfrac{200}{75} \\\\= 2.6[/tex]
Thus, the radius of the wheel would be 2.6 inches.
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