Question

To find the volume of a pyramid you use the formula v=1/3bh. which equation solves this formula for b

Answer 1

We use Justin Bieber's Theorem of "It don't make no sense unless I'm doin' it with you":


`\textbf{The formula } V = (1)/(3)bh \textbf{ has a solution of } b = (3V)/(h)\\\textbf{when solved for b.}`


`\displaystyle V = (1)/(3)bh \\ \\ (dV)/(dV) = (d)/(dV) (1)/(3)bh \\ \\ (dV)/(dV) = (1)/(3)\left(b (dh)/(dV) + h(db)/(dV) \right) \\ \\ 3(1)= b (dh)/(dV) + h(db)/(dV) \\ \\ 3 - h(db)/(dV) = b (dh)/(dV) \\ \\ \\ b = (3 - h(db)/(dV) )/( (dh)/(dV) )`

It can be shown that
`3 - h(db)/(dV) = 3v` and
`(dh)/(dV) = h` so therefore
`b = (3V)/(h)`

Answer 2

I’ll show you step by step:

v=1/3bh

Multiplying both sides by 3:

3v=bh

Dividing both sides by h:

3v/h=b

Therefore,

b=3v/h