Question

Which formula shows a joint variation?

Answer 1

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:

$y=kxz$

Where $x,y$ and $z$ are the variables and $k$ is the constant of proportionality.

As you can see, $y$ is directly proportional to $x$ and $z$.

2. Keeping the information above, you have:

I) $V=lwh$ ($V$ varies jointly with $l$, $w$ and $h$.

II) $V=\frac{1}{3}r^{2}h\pi$ (If $\frac{\pi}{3}$ is the constant of proportionality, $V$ varies jointly with $r^{2}$ and $h$).

III) $V=Bh$ ($V$ varies jointly with $B$ and $h$.

Answer 2

Answer : I, II and III  

To find volume formula that shows joint variation we analyze each option

Joint variation always depends on atleast two dependent variables

for example y = kxy

The variable y depends on x  and y and k is constant of proportionality

V= lwh

It means volume depends on length , width and height. 1 is the constant of  proportionality .

$v=\frac{1}{3} \pi r^2h$

V depends on radius r  and height h. Here 1/3 pi is the constant of proportionality

V= BH

V depend on base b  and height h . 1 is the  constant of  proportionality .

So answer is I, II , III