Thank you for visiting A circle has a radius of 10 centimeters Suppose an arc on the circle has a length of 8 tex pi tex centimeters What is. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
The central angle corresponding to an arc length of 8π cm on a circle with a radius of 10 cm is [tex]\(\frac{4\pi}{5}\)[/tex] radians or 144 degrees. This utilizes the formula relating arc length, radius, and the central angle in radians.
To find the measure of the central angle whose radii define the arc, we can use the relationship between the arc length, the radius of the circle, and the central angle. The formula for the arc length (s) is:
s = rθ
r represents the radius and θ represents the center angle in radians. Given the radius, r = 10 cm, and the arc length, s = 8π cm, we can solve for θ:
- Start with the equation: [tex]\[ 8\pi = 10\theta \][/tex]
- Divide both sides by 10 to isolate θ: [tex]\[ \theta = \frac{8\pi}{10} \][/tex]
- Simplify the equation: [tex]\[ \theta = \frac{4\pi}{5} \][/tex]
So, the measure of the central angle is [tex]\(\frac{4\pi}{5}\)[/tex] radians, which can be converted to degrees if needed (approximately 144 degrees).
The central angle corresponding to an arc length of 8π centimeters on a circle with a radius of 10 centimeters is [tex]\(\frac{4\pi}{5}\)[/tex] radians or 144 degrees. This problem utilizes the formula relating arc length, radius, and the central angle in radians.
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Rewritten by : Jeany
Answer:
The measure of the central angle whose radii define the arc is [tex]\mathbf{\frac{4\pi }{5} }[/tex]
Step-by-step explanation:
Radius of circle = 10 cm
Length of arc = [tex]8\pi[/tex]
We need to find Theta [tex]\theta[/tex]
The formula used will be: [tex]S=r \theta[/tex]
S= length of arc, r = radius and [tex]\theta[/tex] = angle
Putting values and finding \theta
[tex]S=r \theta\\8\pi =10 \theta\\\theta=\frac{8\pi }{10} \\\theta=\frac{4\pi }{5}[/tex]
So, the measure of the central angle whose radii define the arc is [tex]\mathbf{\frac{4\pi }{5} }[/tex]
