The answer is the first option: I, II and III.
The explanation is shown below:
1. By definition, there is a joint variation when a variable depends on two or more different variables. Therefore, you can express it as following:
[tex]y=kxz[/tex]
Where [tex]x,y[/tex] and [tex]z[/tex] are the variables and [tex]k[/tex] is the constant of proportionality.
As you can see, [tex]y[/tex] is directly proportional to [tex]x[/tex] and [tex]z[/tex].
2. Keeping the information above, you have:
I) [tex]V=lwh[/tex] ([tex]V[/tex] varies jointly with [tex]l[/tex], [tex]w[/tex] and [tex]h[/tex].
II) [tex]V=\frac{1}{3}r^{2}h\pi[/tex] (If [tex]\frac{\pi}{3}[/tex] is the constant of proportionality, [tex]V[/tex] varies jointly with [tex]r^{2}[/tex] and [tex]h[/tex]).
III) [tex]V=Bh[/tex] ([tex]V[/tex] varies jointly with [tex]B[/tex] and [tex]h[/tex].
