So we have a tetrahedral pyramid with side length

**a**. What's the volume of the inscribed sphere that is tangent to the sides of the pyramid?

I just need some feedback on a solution, as I have no idea if it is correct. And I should mention that all the faces are equilateral triangles.

Start by solving for the height of each triangular face, with side length

**a**.

where

**k** is the height of one of our face triangles.

Solving,

Now, we can use

**k** to solve for the height of the pyramid,

**h**; imagine a new triangle cutting the pyramid in half.

..... **<<<<< this can't be correct. See attachment.**
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