To find the area of the segment, we first need to find the length of the chord formed by the central angle of 700° in a circle with a diameter of 20 cm.
The length of the chord can be found using the formula:
Length of chord = 2 * Radius * sin(central angle / 2)
Given that the diameter is 20 cm, the radius is half of the diameter, which is 20 cm / 2 = 10 cm.
Using this information, the length of the chord is:
Length of chord = 2 * 10 cm * sin(700° / 2)
= 2 * 10 cm * sin(350°)
≈ 2 * 10 cm * 0.9397
≈ 18.794 cm
Now, to find the area of the segment, we divide the segment into a triangle and a sector. The area of the segment is the difference between the area of the sector and the area of the triangle.
The sector's area can be found using the formula:
Area of sector = (central angle / 360°) * π * Radius²
Given that the central angle is 700° and the radius is 10 cm, the sector's area is:
Area of sector = (700° / 360°) * π * (10 cm)²
= (7/ 36) * π * 100 cm²
≈ 61.62 cm²
The triangle's area can be found using the formula:
Area of triangle = (1/2) * Length of chord * Radius
Given that the length of the chord is 18.794 cm and the radius is 10 cm, the triangle's area is:
Area of triangle = (1/2) * (18.794 cm) * (10 cm)
≈ 93.97 cm²
Finally, the area of the segment is:
Area of segment = Area of sector - Area of triangle
= 61.62 cm² - 93.97 cm²
≈ -32.35 cm²
However, a negative area is not physically possible for a circle segment. Therefore, there may be an error in the given information or calculations. Please double-check your numbers and confirm the values.
Find the area in cm2 of the segment of a circle whose diameter is 20 cm and the central angle measures 700.
1 answer