MATHEMATICS

JAMB 2004 - Question 28

Mathematics 2004 JAMB Past Questions - Question 28: An arc of circle of length 22cm subtends an angle of 3x at the center of teh circle .Find the value of x if the diameter of the circle is 14cm.

An arc of circle of length 22cm subtends an angle of 3x at the center of teh circle .Find the value of x if the diameter of the circle is 14cm.
A:
B:
C:
D:
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Correct Answer

B

Explanation

The length of an arc of a circle is given by the formula:Length of arc = (θ/360) * 2πrwhere θ is the central angle in degrees, r is the radius of the circle, and 2πr is the circumference of the circle.In this case, we are given that the length of the arc is 22 cm and the diameter of the circle is 14 cm. Since the diameter is twice the radius, the radius of the circle is 14/2 = 7 cm.Substituting the given values into the formula, we have:22 = (3x/360) * 2π * 7Simplifying, we get:22 = (3x/360) * 14πDividing both sides by 14π, we have:22 / (14π) = 3x/360Simplifying further, we get:22 / (14π) = x/120To find the value of x, we can cross-multiply:x = (22 / (14π)) * 120x ≈ 24.77Therefore, the value of x is approximately 24.77.