Question

if a wheel rolls a distance of 75 inches as it turns through an angle of 200, what is the radius of the wheel?

Answer 1

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.

How to find the relation between angles subtended by the arc, the radius, and the arc length?

$2\pi^c = 360^\circ = \text$ {Full circumference}

The superscript 'c' shows the angle measured is in radians.

If the radius of the circle is of r units, then:

$1^c \: \rm covers \: \dfrac{circumference}{2\pi} = \dfrac{2\pi r}{2\pi} = r\\\\or\\\\\theta^c \: covers \:\:\: r \times \theta \: \rm \text{units of arc}$

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

$\dfrac{200}{75} \\\\= 2.6$

Thus, the radius of the wheel would be 2.6 inches.

Learn more about angle, arc length relation here:

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