Complete Question
A circle with a 32 inch diameter has a central angle that intercepts an arc measuring approximately 75.36 inches. Which option describes how to determine this angles measure in radians?
A. Divide 75.36 by 16
B. Divide 75.36 by 32
C. Divide 16 by 75.36
D. Divide 32 by 75.36
Answer:
A. Divide 75.36 by 16
Step-by-step explanation:
The formula for Arc length is given as:
S = r θ
Where S = arc length
r = radius
We are told that:
Diameter of a circle = 32 inches
Radius of a circle = Diameter/2
= 32/2 = 16
Arc Length = 75.36 centimeters
The formula for Central angle =
θ = Central angle
θ = S/r
= 75.36/16
Option A is correct
The correct answer is option A. which is Divide 75.36 by 16
A circle is a two-dimensional geometry on the plane having a centre point and the circular line is drawn equidistant from the centre point.
The formula for Arc length is given as:
S = r θ
Where S = arc length
r = radius
We are told that:
Diameter of a circle = 32 inches
The radius of a circle = Diameter/2
r = 32/2 = 16
Arc Length = 75.36 centimeters
The formula for Central angle =
θ = Central angle
θ = S/r
θ= 75.36/16
Therefore the correct answer is option A. which is Divide 75.36 by 16
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