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