WAEC 2017 Mathematics · Question 8

Water flows out of a pipe at a rate of 40 cm^2 per seconds into an empty cylinder container of base radius…

Question

Water flows out of a pipe at a rate of 40 $\pi cm^2$ per seconds into an empty cylinder container of base radius 4cm. Find the height of water in the container after 4 seconds.

A.10 cm
B.14 cm
C.16 cm
D.20 cm

Answer: A. 10 cm

Explanation written with AI and checked against the answer key

Analyze the question: Water flows in at a rate of 40π cm² per second (strictly, a flow rate should be in cm³/s, so we treat it as 40π cm³/s, which is what the question intends). The container is a cylinder with base radius 4 cm. We need the height of water after 4 seconds. Concept: The volume of water in a cylinder is V = πr²h. Volume collected = rate × time. Solution: Step 1: Volume after 4 seconds V = 40π × 4 = 160π cm³ Step 2: Equate to the cylinder volume formula πr²h = 160π π(4²)h = 160π 16πh = 160π Step 3: Solve for h h = 160π ÷ 16π = 10 cm Answer: The height of water is 10 cm, which is option A. Tip: Whenever water fills a cylinder, use "volume in = πr²h". The π cancels out on both sides, which saves you time in the exam. Also, don't be thrown off by the unit written as cm² in the question; treat the rate as a volume per second.

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