AoPS Wiki talk:Problem of the Day/June 22, 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 $(\frac{5}{7})^3$=$\frac{125}{343}$.

Using the formula for the sum of an infinite geometric sequence, $\frac{a}{1-r}$, where $a$ is the first term, and $r$ is the common ratio, we have $\frac{27}{1-\frac{125}{343}}$.

That simplifies to $\boxed{\frac{9261}{218}}$, which is the volume.

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