Thank you for visiting A circle has a radius of 10 centimeters Suppose an arc on the circle has a length of 8 centimeters What is the measure of. 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 :
To find the measure of the central angle whose radii define the arc on a circle, you can use the formula:
\[ \text{Central Angle} = \left( \frac{\text{Arc Length}}{\text{Circle Circumference}} \right) \times 360^\circ \]
Given:
- Radius of the circle = 10 centimeters
- Arc length = 8 centimeters
First, calculate the circle's circumference using the formula:
\[ \text{Circle Circumference} = 2 \times \pi \times \text{Radius} \]
Substitute the radius value:
\[ \text{Circle Circumference} = 2 \times \pi \times 10 = 20\pi \]
Now, substitute the arc length and circle circumference into the central angle formula:
\[ \text{Central Angle} = \left( \frac{8}{20\pi} \right) \times 360^\circ \]
Simplify the fraction:
\[ \text{Central Angle} = \left( \frac{2}{5\pi} \right) \times 360^\circ \]
To find the answer, calculate the value:
\[ \text{Central Angle} ≈ 72.57° \]
Rounded to the nearest whole number, the measure of the central angle whose radii define the arc is approximately 73 degrees. Therefore, the closest option among the choices provided is 72 degrees.
\[ \text{Central Angle} = \left( \frac{\text{Arc Length}}{\text{Circle Circumference}} \right) \times 360^\circ \]
Given:
- Radius of the circle = 10 centimeters
- Arc length = 8 centimeters
First, calculate the circle's circumference using the formula:
\[ \text{Circle Circumference} = 2 \times \pi \times \text{Radius} \]
Substitute the radius value:
\[ \text{Circle Circumference} = 2 \times \pi \times 10 = 20\pi \]
Now, substitute the arc length and circle circumference into the central angle formula:
\[ \text{Central Angle} = \left( \frac{8}{20\pi} \right) \times 360^\circ \]
Simplify the fraction:
\[ \text{Central Angle} = \left( \frac{2}{5\pi} \right) \times 360^\circ \]
To find the answer, calculate the value:
\[ \text{Central Angle} ≈ 72.57° \]
Rounded to the nearest whole number, the measure of the central angle whose radii define the arc is approximately 73 degrees. Therefore, the closest option among the choices provided is 72 degrees.
Thank you for reading the article A circle has a radius of 10 centimeters Suppose an arc on the circle has a length of 8 centimeters What is the measure of. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!
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