Find the area of a circular segment of a circle of radius 7cm that sub tends a central angle of 35 degrees?
area of sector/area of circle = 35/360
area of sector /49π = 7/72
area of sector = 343π/72
area of triangle with the chord as its base
= (1/2)(7)(7)sin35°
= (49/2)sin35 , Using area of triange = (1/2)(a)(b)sinØ
where a and b are sides with Ø the contained angle
area of segment = 343π/72 - (49/2)sin35°
= ....
you do the button-pushing if you need a decimal answer
HEIP ME ANSWER THIS QUESITION.A PERIMETER OF A SECTOR OF A CIRCLE OF RADIUS 7CM WHICH SUBTENDS ANGLE 6ODEGREE AT CENTRE
To find the area of a circular segment, we need to know the radius of the circle and the central angle that the segment subtends.
In this case, the given radius is 7 cm, and the central angle is 35 degrees.
To find the area of the circular segment, we will follow these steps:
1. Convert the central angle from degrees to radians.
- Since 1 radian is equal to 180/π degrees, we can convert the angle as follows:
- Angle in radians = Angle in degrees * (π/180)
- Substituting the given angle, we get:
- Angle in radians = 35 * (π/180)
- Angle in radians ≈ 0.6109
2. Find the length of the circular arc that forms the segment.
- The length of the arc can be calculated using the formula:
- Arc length = Radius * Angle in radians
- Substituting the given radius and angle, we get:
- Arc length = 7 cm * 0.6109
- Arc length ≈ 4.2773 cm
3. Find the area of the circular segment.
- The area of the segment can be calculated as the difference between the sector area and the triangular area.
- Sector area = (θ/2) * Radius^2
- Triangular area = (1/2) * Base * Height
- Substituting the values, we get:
- Sector area = (0.6109/2) * (7 cm)^2 ≈ 12.6178 cm^2
- Triangular area = (1/2) * 4.2773 cm * 7 cm ≈ 14.9925 cm^2
- Area of the segment ≈ Sector area - Triangular area
- Area of the segment ≈ 12.6178 cm^2 - 14.9925 cm^2
- Area of the segment ≈ -2.3747 cm^2
Therefore, the area of the circular segment, in this case, is approximately -2.3747 cm^2. Note that a negative area would not make physical sense in this context, so it would be reasonable to review the calculations and ensure accurate input of data.