Water and marbles in a boiling tube

Water and marbles in a boiling tube

Secondary 2
TGM Original Questions

A boiling tube consists of a hemisphere of radius 3 cm attached below a cylinder of the same radius and height 10 cm. Use \(\pi=3.142\).

  1. It contains \(150\text{ cm}^3\) of water. Find
    1. the water height in the cylindrical part,
    2. total depth from the tube bottom.
  2. Six marbles of volume \(8\text{ cm}^3\) each are immersed; find the rise.
  3. Find the tube’s inner surface area.
  4. If cylinder height increases by 10%, find the percentage increase in inner area.

Solution:

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Answer:(a)(i) \(3.30\) cm; (ii) \(6.30\) cm; (b) \(1.70\) cm; (c) \(245.08\text{ cm}^2\); (d) \(7.69\%\).

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