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What is the ratio of the volume of a tetrahedron A to the volume of that tetrahedron B which is formed by joining the centroids of the four triangles forming the tetrahedron A?

Note by Alekhya China 2 years ago

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2 \times 3

2^{34}

a_{i-1}

\frac{2}{3}

\sqrt{2}

\sum_{i=1}^3

\sin \theta

\boxed{123}

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Note that tetrahedrons A and B are similar and B is smaller by a factor of 3.

Hence, the required ratio is \(3^3=\boxed{27}\)

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EXCELLENT ANSWER!

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Easy Math Editor

`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

`> This is a quote`

Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

`\frac{2}{3}`

`\sqrt{2}`

`\sum_{i=1}^3`

`\sin \theta`

`\boxed{123}`

## Comments

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TopNewestNote that tetrahedrons A and B are similar and B is smaller by a factor of 3.

Hence, the required ratio is \(3^3=\boxed{27}\)

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EXCELLENT ANSWER!

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