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Analysing Scientific Interrelationships - Example 6
Instructions
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
A set square comprises a ruler and an angle gauge (a scale for measuring angles).
This particular set square consists of a material which has expanded homogeneously by
1 percent in all lengths since it (the set square) was manufactured.
Which of the two statements is or are correct?
I. When measuring length, the values shown by the ruler are too small.
II. The circumference of the set square has increased by 3 percent.
Degree of difficulty: high
Solution
Let us assume the numbers on the upper edge (base edge) of the set square give the length
in centimetres (cm). Then the distance between the “5” on the left side and the “5” on the
right side – if measured with a normal set square or ruler – would measure 10.0 cm (5.0 + 5.0).
When the set square has expanded by 1 percent, this distance measures 10.1 cm. If one uses this
set square to measure an object which is exactly 10.0 cm long, this object will not reach all
the way from the one “5” to the other “5”.
The set square will accordingly show a value which
is somewhat smaller than 10.0. Statement I is therefore correct. (This train of thought
is somewhat easier to follow if one imagines an expansion of – for example – 50 percent.)
If each of the three sides of the set square increases by one percent, then the overall circumference
also increases by 1 percent. Statement II is therefore wrong.
Therefore (A) is correct.
Instructions
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
