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Carlos builds a robot that moves with small wheels. each wheel has six 5 inch long metal spokes that meet in the center what is the length of the arc

Carlos builds a robot that moves with small wheels. each wheel has six 5 inch long-example-1
User Bi Li
by
3.1k points

1 Answer

27 votes
27 votes

Answer:

Step-by-step explanation:

a)

The formula for calculating the length of an arc is expressed as

Length of arc = θ/360 x 2πr

where

θ is the angle subtended at the center of the circle.

r is the radius of the circle

From the information given,

diameter = 5(length of each metal spoke)

r =diameter/2 = 5/2 = 2.5

Recall, the total angle in the circle is 360 degrees. There are 8 partitions. Angle between consecutive spokes is

360/8 = 45. Thus,

θ = 45

Length of are between consecutive spokes = 45//360 x 2 x π x 2.5

Length of are between consecutive spokes = 5π/8

b) The formula for calculating the area of a sector is expressed as

area of a sector = θ/360 x πr^2

By substituting the values,

area of a sector = 45/360 x π x 2.5^2

Area of sector = 25π/32 square inches

User Carsten Massmann
by
2.8k points
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