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Problem of the Week
Problem B and Solution
What’s Beneath the Surface?

Problem

In each problem below, use the information given about part of the object’s mass to determine the unknown mass.

  1. Contrary to what you may have heard, ostriches do not bury their heads in the sand. But, if one decided to do so just for fun, and its \(2000\,\)g head was \(2\%\) of its total body mass, then what would be the mass of its entire body, in kilograms?

  2. Generally, about \(90\%\) of an iceberg’s mass is below water level. If the mass of the visible portion of a certain iceberg is \(50\,000\,\)tonnes, then what is the mass of the whole iceberg, in tonnes?

  3. Only a small portion of a growing mushroom is visible; most of the fungus is below the ground. If \(5\%\) of a mushroom is above the ground, and this portion has a mass of \(100\,\)g, then what is the mass of the mushroom below the ground, in kilograms?

Solution

  1. We’re given that \(2\%\) of the ostrich’s mass is \(2000\) g. Since \(2\% \times 50 = 100\%\), the total mass of the ostrich must be \(2000 \times 50=100\,000\) g, or \(100\) kg.

  2. Given that \(90\%\) of an iceberg is hidden, the visible mass must be \(100\%-90\%=10\%\) of its total mass. Thus, if the visible portion is \(50\,000\) tonnes, and since \(10\% \times 10 = 100\%\), the total mass must be \(50\,000\times 10= 500\,000\) tonnes.

  3. If \(5\%\) of the mushroom is above the ground, then \(100\%-5\%=95\%\) of the mushroom is below the ground. Since \(5\% \times 19 = 95\%\), the portion of the mushroom below the ground must have a mass of \(100 \times 19 = 1900\) g, or \(1.9\) kg.

    Alternatively, the visible portion of the mushroom has a mass of \(100\) g, which is \(5\%\) of its total mass. Since \(5\% \times 20 = 100\%\), the total mass of the mushroom must be \(100 \times 20=2000\) g. Then the portion of the mushroom below the ground must have a mass of \(2000-100=1900\) g, or \(1.9\) kg.