Thank you for visiting Consider circle C with a radius of 5 cm and a central angle measure of 60 Circle C is shown Line segments RC and SC. 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 fraction of the whole circle is arc RS = (1/6)
approximate circumference of the circle = 31.4 cm
approximate length of arc RS = 5.23 cm
What is a circle?
A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point.
As per the given data:
Radius of circle with center C = 5 cm
central angle = 60°
∠RCS = 60°
To find out the fraction of the whole circle is arc RS:
arc length = radius × θ {θ is in radians}
∠RCS = 60° = 60° × (π/180°) = π/3
fraction of the whole circle = arc length / circumference
= [tex]\frac{r \times \frac{\pi}{3}}{2\pi r}[/tex] = (1/6)
approximate circumference of the circle = 2πr
= 2π(5)
= 31.4 cm
approximate length of arc RS = r × θ
= 5 × (π/3)
= 5.23 cm
Hence, the fraction of the whole circle is arc RS = (1/6)
approximate circumference of the circle = 31.4 cm
approximate length of arc RS = 5.23 cm
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Final answer:
Explanation of fraction of the circle represented by an arc, the approximate circumference of a circle, and the approximate length of an arc.
Explanation:
Fraction: The fraction of the whole circle that arc RS represents can be calculated using the central angle measure. Since the central angle is 60°, which is 1/6 of the total 360° in a circle, the fraction of the circle represented by arc RS is 1/6.
Circumference: The approximate circumference of a circle can be calculated using the formula C = 2πr, where r is the radius. Substituting r = 5 cm, the circumference is approximately 10π cm.
Arc Length: To find the approximate length of arc RS, we use the formula for arc length: Arc Length = (θ/360) x 2πr, where θ is the central angle. Substituting θ = 60° and r = 5 cm, the length of arc RS is approximately 5π/3 cm.
