Difference between revisions of "AoPS Wiki talk:Problem of the Day/June 22, 2011"
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+ | The total volume can be expressed as the sum of an infinite geometric sequence where the common ratio is <math>(\frac{5}{7})^3</math>=<math>\frac{125}{343}</math>. | ||
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+ | Using the formula for the sum of an infinite geometric sequence, <math>\frac{a}{1-r}</math>, where <math>a</math> is the first term, and <math>r</math> is the common ratio, we have <math>\frac{27}{1-\frac{125}{343}}</math>. | ||
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+ | That simplifies to <math>\boxed{\frac{9261}{218}}</math>, which is the volume. |
Latest revision as of 19:02, 22 June 2011
Problem
AoPSWiki:Problem of the Day/June 22, 2011
Solutions
The total volume can be expressed as the sum of an infinite geometric sequence where the common ratio is =.
Using the formula for the sum of an infinite geometric sequence, , where is the first term, and is the common ratio, we have .
That simplifies to , which is the volume.