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I have attached the question

we can do this

yes, could you explain it ?

ok first off z is 4, so lets forget z and replace it by 4

the volume of the first tube, the one with side \(x\) is \(4\times (\frac{1}{4}x)^2\)

why is it 1/4 ?

ok

ok?

the volume of the second one is easy, since \(z=4\) it is just \(y\)

ok

then we add them togther?

now we use the fact that \(x+y=8\) and so \(y=8-x\)

got it

i guess it is \([0,8]\) since \(x\) must be in there somewhere

ok, thanks alot `