Practical Mathematics Stage I

Cover Practical Mathematics Stage I
Practical Mathematics Stage I
A G Alfred George Cracknell
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Example. The circumference of a circle varies directly as its diameter; and when the diameter is 21 inches the circumference is 66 inches: find the circumference when the diameter is 35 inches.
Let O and D represent the circumference and diameter respectively.
Then CocD . *. C = wD, where m is some constant but when D is 21, C = 66 . *. 66 = m x 21 hence m f = ^ /. C s *j* D [This equation gives the actual relation between the circumference and diameter of any circle. ] Thus when D is 35 C = yt
... x 35 = 1 10 inches 108. We will work one or two more examples on direct variation by the latter method.
Example (i). The volume of a sphere varies as the cube of its diameter ; when the diameter is I inch, the volume is '5326 cub. Inch : find the volume zvhen the diameter M2'J inches.
Let V represent the volume and D the diameter, then V D 3 ; thus V = m D 3, where m is constant but when D = 1, V = '5236 . *. "5236 = m x 1 i. E. M = '5236 hence V = '5236 D 3 [This equation gives the actual relation between the volume and diameter of a sphere .


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