anonymous
  • anonymous
Match each set of measures of a and b with the measure of c that gives a volume of 24 cubic inches. a = 2in and b = 8 in a = 4in and b = 2 in a = 3in and b = 4 in a = 6in and b = 4in options are A. c = 2 in B. c = 3 in C. c = 4 in D. c = 6 in
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
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Directrix
  • Directrix
The volume of a triangular base prism is the area of its base times its height. In this problem, the area of the base is 1/2 (a*c) and the height is b. So, Volume = 1/2 (a*c)*b or 1/2 (a*b*c). Note that the volume is 24. If 24 = 1/2 (a*b*c), then 48 = (a*b*c). Choosing the value of c is reduced to finding a number that when multiplied by a*b gives 48. On the uploaded chart, look at the first row. a = 2 and b = 8. a*b = 16. So, what times 16 = 48. That is 3 which appears on the row under the "c" column. Using that strategy, the other values of c can be found without a lot of work. Last, the matching.
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