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Dimensional Analysis & Metric Calculations Flashcards

6 cards from real CMS practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

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  1. A pipe carries fluid at a flow rate of 300 L/min. Convert this to m³/s:

    Answer: 0.005 m³/s

    300 L/min × (1 m³/1,000 L) × (1 min/60 s) = 300/60,000 = 0.005 m³/s.

  2. What is 0.5 m² expressed in cm²?

    Answer: 5,000 cm²

    1 m = 100 cm, so 1 m² = 10,000 cm²; therefore 0.5 m² = 5,000 cm².

  3. The specific heat capacity of water is 4,186 J/(kg·K). How much energy is needed to heat 2 kg of water by 10 K?

    Answer: 83,720 J

    Q = mcΔT = 2 kg × 4,186 J/(kg·K) × 10 K = 83,720 J.

  4. If a conversion factor is written as a fraction equal to 1 (e.g., 1 kg/1,000 g), it is called a:

    Answer: Unity fraction

    A unity fraction is a conversion factor expressed as a fraction equal to 1, used in dimensional analysis to cancel units.

  5. A cylindrical tank has a radius of 0.5 m and a height of 2 m. What is its volume in litres? (V = πr²h)

    Answer: 1,571 L

    V = π × 0.5² × 2 = π × 0.25 × 2 ≈ 1.571 m³ = 1,571 L (1 m³ = 1,000 L).

  6. A sprint track is 400 m long. How many laps equal exactly 1 km?

    Answer: 2.5 laps

    1 km = 1,000 m; 1,000 m ÷ 400 m/lap = 2.5 laps.