6. Find the area of the sector below. Show all work! Leave your answer in terms of T. Label your answers with units and simplify the fraction fully. 60° 14 cm
Angles in Circles
Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.
Arcs in Circles
A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.
![### Problem 6: Find the Area of the Sector Below
**Instructions:** Show all work! Leave your answer in terms of π. Label your answers with units and simplify the fraction fully.
#### Given Data:
- Central angle of the sector: 60°
- Radius of the circle: 14 cm
#### Diagram:
The diagram shows a circle with a shaded sector. The sector has a central angle of 60°. The radius of the circle is labeled as 14 cm.
#### Solution:
To find the area of a sector of a circle, use the formula:
\[ A = \pi r^2 \left( \frac{\theta}{360} \right) \]
Where:
- \( A \) is the area of the sector.
- \( r \) is the radius of the circle.
- \( \theta \) is the central angle in degrees.
Substitute the given values into the formula:
- \( r = 14 \) cm
- \( \theta = 60^\circ \)
\[ A = \pi (14)^2 \left( \frac{60}{360} \right) \]
\[ A = \pi (196) \left( \frac{1}{6} \right) \]
\[ A = \pi \left( \frac{196}{6} \right) \]
\[ A = \pi \left( \frac{98}{3} \right) \]
Therefore, the area of the sector is:
\[ \boxed{\frac{98\pi}{3} \text{ cm}^2} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F655ac9a1-7c8e-4ab3-b40b-8b818745323f%2Fd232cafb-4932-4251-bd14-5b3213944308%2F1xo4y7_processed.png&w=3840&q=75)
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