MATHEMATICS

JAMB 2002 - Question 28

Mathematics 2002 JAMB Past Questions - Question 28: A chord of a circle subtends an angle of 120 at the center of a circle of diameter 4√3cm. Calculate the area of the major sector.

A chord of a circle subtends an angle of 120 at the center of a circle of diameter 4√3cm. Calculate the area of the major sector.
A:
B:
C:
D:
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Correct Answer

A

Explanation

The angle subtended by the chord at the center of the circle is 120 degrees. Since the diameter of the circle is 4√3 cm, the radius of the circle is half of the diameter, which is 2√3 cm.To calculate the area of the major sector, we need to find the length of the arc and the area of the corresponding sector.The length of the arc can be calculated using the formula:Arc Length = (θ/360) * 2πrwhere θ is the angle in degrees and r is the radius of the circle.Arc Length = (120/360) * 2π * 2√3          = (1/3) * 2π * 2√3          = (2/3)π√3 cmThe area of the sector can be calculated using the formula:Sector Area = (θ/360) * πr²Sector Area = (120/360) * π * (2√3)²            = (1/3) * π * 12            = 4π cm²Therefore, the area of the major sector is 4π cm².