I believe this is a typo, but just in case.

[Ana.stasia]

I needed to calculate the height of a regular tetrahedron only by using the volume. I did not have any numbers. The point was just that the solution must only include the volume symbol and nothing else.

Here is how I did it.



The only difference between my solution and the solution from the book is that I have a square root of 2 and they have the square root of three. I believe this is a typo because the solutions are way too similar. However, just in case I wanted to check. Did I make a mistake?

Thank you in advance

 

[Dr.Peterson]

Let's just check the answer. When I look up formulas for the regular tetrahedron, I find

[MATH]V = \frac{\sqrt{2}}{12}a^3[/MATH]​

[MATH]h = \frac{\sqrt{6}}{3}a[/MATH]​

Solving the first for a, and putting that into the second, I get

[MATH]a = \sqrt[3]{\frac{12V}{\sqrt{2}}}[/MATH]​

[MATH]h = \frac{\sqrt{6}}{3}\sqrt[3]{\frac{12V}{\sqrt{2}}} = \sqrt[3]{\frac{6\sqrt{6}}{27}\frac{12V}{\sqrt{2}}} = \sqrt[3]{\frac{8\sqrt{3}V}{3}} = 2\sqrt[3]{\frac{\sqrt{3}V}{3}}[/MATH]​

So their answer is correct. Look through your work (I haven't yet) and see if you can find an error.

 

[Ana.stasia]

Thank you. I did find an error.