The volume of a square pyramid

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silverdragon316

Junior Member
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Mar 16, 2007
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This is the problem:

The volume of a square pyramid is:v=1/3s^2h..........s=length of a side,h=height.
solve for s.

I know you have to get everything but s to one side.
You also have to multiply to get fractions to the other side.

v=1/3s^2h
3v=s^2h
3v-h=s^2
3v-h=s
....s

is this correct? If not what did I do wrong?
 
You are incorrect.

I think the formula is: \(\displaystyle \L \;v\,=\,\frac{1}{3}s^{2}h\)

You're right about multiplying by 3:\(\displaystyle \L \;3v\,=\,s^{2}h\)

Now we must divide by h:\(\displaystyle \L \;\frac{3v}{h}\,=\,s^2\)

\(\displaystyle \L \;s\,=\,\sqrt{\frac{3v}{h}}\)
 
jonboy said:
You are incorrect.

I think the formula is: \(\displaystyle \L \;v\,=\,\frac{1}{3}s^{2}h\)

You're right about multiplying by 3:\(\displaystyle \L \;3v\,=\,s^{2}h\)

Now we must divide by h:\(\displaystyle \L \;\frac{3v}{h}\,=\,s^2\)

\(\displaystyle \L \;s\,=\,\sqrt{\frac{3v}{h}}\)
Click to expand...
Why or how does it become squared? :?
 
The inverse (or the opposite operation of a number that will cancel it) of a square is the square root. Just like the inverse of adding is subtracting.

So when I have s^2 and I square root both sides of the equation it gets rid of the square on the s.

More detailedly:

\(\displaystyle \L \;s^2\,=\,\frac{3v}{h}\)

\(\displaystyle \L \;\sqrt{s^2}\,=\,\sqrt{\frac{3v}{h}\)

Since there's nothing on the right side of the equal sign to simplify in the square root to simplify you keep it there:

\(\displaystyle \L \;s\,=\,\sqrt{\frac{3v}{h}}\)
 
"s" was squared in the original formula ... it represents the area of the square base.
 
skeeter said:
"s" was squared in the original formula ... it represents the area of the square base.
Click to expand...
I think silverdragon316 means square root.
 
Your welcome and I'm glad my explanation was good enough to be understood!
 
silverdragon316 said:
The volume of a square pyramid is:v=1/3s^2h..........s=length of a side,h=height.
solve for s.
Click to expand...
The volume of a pyramid is V = 1/3 the product of the base area and the height = b^2h/3 where b = the length of the base side and h = the height.
 
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