WAEC 2014 Mathematics · Question 12

The radii of the base of two cylindrical tins, P and Q are r and 2r respectively. If the water level in p is…

Question

The radii of the base of two cylindrical tins, P and Q are r and 2r respectively. If the water level in p is 10cm high, what would be the height of the same quantity of water in Q?

A.2.5cm
B.5.0cm
C.7.5cm
D.20.0cm

Answer: A. 2.5cm

Explanation written with AI and checked against the answer key

Analyze the question: The same quantity (volume) of water is poured from tin P into tin Q. The radii are different, so the height changes. We need the new height in Q. Concept: Volume of a cylinder = πr²h. Since the water volume stays the same, V(P) = V(Q). Solution: Volume in P = π(r)²(10) = 10πr² Volume in Q = π(2r)²(h) = 4πr²h Equate the volumes: 4πr²h = 10πr² Divide both sides by πr²: 4h = 10 h = 10 ÷ 4 = 2.5 cm Check: Q's base area is 4 times that of P (since (2r)² = 4r²). The water spreads over 4 times the area, so the height is ¼ of 10 cm = 2.5 cm. ✔ Tip: When the same volume moves between cylinders, height is inversely proportional to the square of the radius. If the radius doubles, the height becomes ¼. If the radius triples, the height becomes 1/9. Many students forget to square the radius and wrongly choose 5.0 cm (option B), so watch out for that trap.

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