Arithmetic: in Two Parts: Part 1, Advanced Lessons in Mental Arithmetic ...

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Arithmetic: in Two Parts: Part 1, Advanced Lessons in Mental Arithmetic ...
Frederic a Adams
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In what ratio are their areas? — Let one meas- ure 2 feet on a side ; the other, 6. In what ratio are their areas?
The area of the larger, you find, is 9 times as great as that of the smaller. Ttis may serve to suggest the principle by which the areas of all similar surfaces may be compared.
The areas of similar surfa^ces are to each other as the sqtiares of their corresponding dimensions.
Let one square measure 1 foot on a side ; another, 2 feet. 12 : 2^ : : 1 : 4.
Let one square measure 2 fee
...t, and another, 4 feet, on a side. 2^ : 4^ : : 4 : 16.
Let one square measure 1 foot on a side ; another, 3 feet. V : 32 : : 1 : 9.
Let one square measure 2 feet on a side ; another, 6 feet. 22 : 62 : : 4 : 36.
This principle applies to circles, triangles, and all similar surfaces whatever. You can now recur to question 4, and find the answer to it« y Google COMPARISON OF SIMILAR SOLIDS. 137 6. There are two circles. The diameter of the greater is 3 times that of the smaller. The area of the smaller is 1 acre.


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