Question

4(a). In the diagram, O is the centre of the circle radius r cm and ∠XOY=90°. If the area of the shaded part is 504cm², calculate the value of r. [Take π=22/7]

Accepted Answer

Sector area (90°) = (90/360)πr² = πr²/4
Triangle XOY area = ½r²sin90° = ½r²
Shaded (segment) area = sector − triangle = r²(π/4 − 1/2)
Using π=22/7: π/4−1/2 = 11/14 − 7/14 = 2/7
So: r²×(2/7) = 504
r² = 504×7/2 = 1764
r = √1764 = 42cm

WAEC Mathematics 2014 Theory — Question 7

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