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Arc XY located on circle A has a length of 40 centimeters. The radius of the circle is 10 centimeters. What is the measure of the corresponding central angle for XY in radians?

A. 4

B. [tex]\frac{4}{3} \pi[/tex]

C. 3

D. [tex]\frac{3}{4} \pi[/tex]

Sagot :

GinnyAnswer
To find the measure of the central angle corresponding to an arc on a circle, we use the relationship between the arc length, radius, and central angle. This relationship is given by the formula:

[tex]\[ \theta = \frac{s}{r} \][/tex]

where:
- [tex]\( \theta \)[/tex] is the measure of the central angle in radians,
- [tex]\( s \)[/tex] is the arc length,
- [tex]\( r \)[/tex] is the radius of the circle.

Given:
- The length of arc [tex]\( XY \)[/tex] (s) is 40 centimeters,
- The radius of the circle (r) is 10 centimeters.

Substitute the known values into the formula:

[tex]\[ \theta = \frac{40 \, \text{cm}}{10 \, \text{cm}} \][/tex]

Simplify the fraction:

[tex]\[ \theta = 4 \, \text{radians} \][/tex]

Therefore, the measure of the central angle for arc [tex]\( XY \)[/tex] is 4 radians.

The correct answer is:
A. 4
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