To the right are drawings of a wide and a narrow cylinder. The cylinders have equally spaced marks on them. Water is poured into the wide cylinder up to the 4th mark (see A). This water rises to the 6th mark when poured into the narrow cylinder (see B).Both cylinders are emptied (not shown) and water is poured into the narrow cylinder up to the 11th mark. How high would this water rise if it were poured into the empty wide cylinder?
Correct answer: B. To about 7 1/3
- A. To about 7 1/2
- B. To about 7 1/3
- C. To about 8
- D. To about 9
- E. None of these answers is correct
Explanation
The height of the water when poured into the empty wide cylinder is;Option b; To the 7¹/₃ markFormula for volume of a cylinder is;V = πr²h where;r is radiush is heightWe are told that water is poured into the wide cylinder up to the 4th mark. Thus, for the wide cylinder, h = 4. Thus;V_wide = 4πR²Similarly, we are told that water is poured into the narrow cylinder up to the 6th mark. Thus, for the narrow cylinder, h = 6. Thus;V_narrow = 6πr²Now, the volume of the water will be the same since it was the same quantity that was poured. Thus;V_wide = V_narrow4πR² = 6πr²⇒ R²/r² = 6/4simplifies to get; R²/r² = ³/₂Now both cylinders were emptied and water poured rises to the 11th mark for the narrow cylinder. Thus;πR²H = 11πr²R²/r² = 11/HEarlier, we saw that R²/r² = ³/₂. Thus;11/H = ³/₂H = 22/3H = 7¹/₃
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Scientific reasoning evaluates hypotheses through observations, variables, controls, measurements and experimental results. Questions involve identifying independent and dependent variables, recognising a fair test, interpreting tables or graphs, distinguishing evidence from opinion, and deciding whether data supports, rejects or leaves a hypothesis unresolved.
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