Question

Carlos builds a robot that moves on small wheels. Each wheel has eight 3-inch-long metal spokes that meet in the center.

a) What the length of an arc between two consecutive spokes?
Express your answer as a simplified fraction in terms of
π.

b) What is the area of the sector between these spokes?
Express your answer as a simplified fraction in terms of
π.

C) What is the linear velocity of the outer endpoint of each spoke if it travels 12 feet in 5 seconds?
(round your answer to the nearest tenth)
____________feet/seconds

Answer 1

It should be noted that the length of an arc between two consecutive spokes is 2.3562.

How to calculate the arc

From the information given, the following can be noted:

Radius = 3 inches

Angle of arc = 360°/8 = 45° = π/4

The length of the arc will be:

= π/4 × 3

= 3π/4

= 2.3562

The area of the sector will be:

= πr² × [3π/(4 × 2π)]

= π(3)² × 3π/8π

= 27π/8 inches²

In conclusion, the area of the sector is 27π/8 inches².

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