1. The problem statement, all variables and given/known data
Find the circle segment area that has the boundaries of line segment AB and the minor arc ACB.
Give the area in an exact form in terms of surds and Pi. (see attachments for annotated picture & original question).
2. Relevant equations
Equation 1: Area of a segment = Sector area - Triangle area
Equation 2: Sector area = Central angle/360 * pi * diameter
Equation 3: Triangle area = 0.5 * base * height
3. The attempt at a solution
Area of sector = 120/360 * pi * 4
Simplified = 1/3 * pi/1 * 4/1 = 4/3 * pi [Units squared]
Area of one of the triangle = 0.5 * 1√3 * 1
Combined triangle area = 0.5 √3 x 2 = 1√3
Segment area = (4 * pi/3 - √3) [Units squared]
Approximated answer = 2.4567
Find the circle segment area that has the boundaries of line segment AB and the minor arc ACB.
Give the area in an exact form in terms of surds and Pi. (see attachments for annotated picture & original question).
2. Relevant equations
Equation 1: Area of a segment = Sector area - Triangle area
Equation 2: Sector area = Central angle/360 * pi * diameter
Equation 3: Triangle area = 0.5 * base * height
3. The attempt at a solution
Area of sector = 120/360 * pi * 4
Simplified = 1/3 * pi/1 * 4/1 = 4/3 * pi [Units squared]
Area of one of the triangle = 0.5 * 1√3 * 1
Combined triangle area = 0.5 √3 x 2 = 1√3
Segment area = (4 * pi/3 - √3) [Units squared]
Approximated answer = 2.4567
0 commentaires:
Enregistrer un commentaire