Question

4. (a) The area of a circle is 154cm². It is divided into three sectors such that two of the sectors are equal in size and the third sector is three times the size of the other two put together. Calculate the perimeter of the third sector. [Take π=22/7]

Accepted Answer

Area = πr² ⇒ 154 = (22/7)r² ⇒ r² = (154×7)/22 = 49 ⇒ r = 7cm.
Let each of the two equal sectors have angle θ. Third sector = 3(θ+θ) = 6θ. Sum of angles at centre: 6θ+θ+θ=360° ⇒ 8θ=360° ⇒ θ=45°. Third sector angle = 6×45°=270°.
Arc length of third sector = (θ/360°)×2πr = (270/360)×2×(22/7)×7 = 33cm.
Perimeter of third sector = arc length + 2 radii = 33+7+7 = 47cm.

WAEC Mathematics 2013 Theory — Question 4

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