Question

3(a) In the diagram above, ∠RTS=28°, ∠VRM=46°, MQ is a tangent to the circle VRSTU at the point R. Find ∠VUS.
(b) A cylinder tin, 7cm high, is closed at one end. If its total surface area is 462cm², calculate its radius. [Take π=22/7]

Accepted Answer

(a) ∠VUS is found using circle theorems relating tangent-chord angles and angles in the same segment: ∠VUS = ∠VRM + ∠RTS (exterior angle / alternate segment relationships) = 46° + 28° = 74° (using the given angles and tangent properties of the circle VRSTU).

(b) Since it is closed at only one end, Total surface area = 2πr² + 2πrh (curved surface + one circular end)... 
Using πr² + 2πrh = 462:
πr(r+2h)=462
(22/7)r(r+14)=462
r(r+14)=462×7/22=147
r²+14r-147=0
Using the quadratic formula: r = [-14±√(196+588)]/2 = [-14±28]/2
r = 7cm (taking the positive root).

WAEC Mathematics 2016 Theory — Question 3

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