Question

The figure below shows the ideal pattern of movement of a herd of cattle, with the arrows showing the movement of the handler as he moves the herd. The arc the handler makes from the starting point to the return point should be a quarter of a circle:

A sector showing a quarter of a circle is drawn. The radius is marked as 70 feet. The endpoints of the arc of the sector are marked as Starting Point and Return Point. The sector is filled with cattle.

Based on this theory, what distance will the handler move from the starting point to the return point if he creates an arc of a circle with radius 70 feet?

a
439.6 feet

b
3846.5 feet

c
109.9 feet

d
1758.4 feet

Answer 1

Based on the theory, the distance from the starting point to the return point = Arc length = 109.9 feet.

What is the Length of an Arc?

Arc length = ∅/360 × 2πr

Since the sector formed is a quarter circle, then ∅ = 90°.

Raidus (r) = 70 ft

Distance from the starting point to the return point = arc length.

Arc length = ∅/360 × 2πr =  90/360 × 2π(70)

Arc length = 109.9 feet

Therefore, based on the theory, the distance from the starting point to the return point = Arc length = 109.9 feet.

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