Question

Which formula shows a joint variation?

Answer 1

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=(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

Answer 2

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=(1)/(3)r^(2)h\pi` (If
`(\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`.