Methods 12 Practise SAC help

[zhe0001]

Hey forum,
I've attempted these practise questions but find them difficult. Please show as to how I might get the answer. Thanks!

Q1. A rectangular sheet of metal measuring 10cmX12 cm is to be used to construct an open rectangular tray. the tray will be constructed by cutting out four equal squares from each corner of the sheet.
a. write down the length, width and height of the completed tray in terms of x.
b. show that the volume of the box is given by V=120x - 44x^2 + 4x^3
c. state the domain

Q2. A cone with a slant has a height of 8m, the radius of the base x m and the height h m. The volume of cone is given by 1/3pi^2h
a. show that x = squareroot(64-h^2)
b. show that the volume of the gravel, V in m^3 is V=1/3pih(64-h^2)
c. state the domain for the function

Any help will be appreciated! I'm especially confused with the domain questions.
Thanks!

[Lasercookie]

For Q1, let x be the length of the little square you cut out from the corners. Once you cut out these squares, you fold up the edge bits to form the tray etc. These both are the kind of questions where a diagram really helps.

Any help will be appreciated! I'm especially confused with the domain questions.

The variable that we have is constrained by reality. It's unrealistic to have negative values for length/height, so in these cases we only look at values greater (or equal to) zero. It's also not possible to have a value that's greater than what we started out with. For Q1 we have a 10 x 12 cm sheet of metal, what's the biggest length you can cut out from this?

It's quite similar for Q2, but I think there's some missing information for that question? What's this gravel they're talking about? I'm assuming that we have a cone that's 8m high and has a base with radius x metres. I am then guessing that the cone is then filled with gravel and the height 'h' is the height of the gravel inside the cone. In which case we know what the lower limit for the height of the gravel will be, and the upper limit too (since we can have at most 8 metres of gravel in the cone, any more than that and it'd spill over).

That's a lot of assumptions about the question I'm making though, but either way the idea for deciding the domain for these kind of worded problems is the same, asking what values are realistic and what values are unrealistic.

[zhe0001]

For Q1, let x be the length of the little square you cut out from the corners. Once you cut out these squares, you fold up the edge bits to form the tray etc. These both are the kind of questions where a diagram really helps.
The variable that we have is constrained by reality. It's unrealistic to have negative values for length/height, so in these cases we only look at values greater (or equal to) zero. It's also not possible to have a value that's greater than what we started out with. For Q1 we have a 10 x 12 cm sheet of metal, what's the biggest length you can cut out from this?

It's quite similar for Q2, but I think there's some missing information for that question? What's this gravel they're talking about? I'm assuming that we have a cone that's 8m high and has a base with radius x metres. I am then guessing that the cone is then filled with gravel and the height 'h' is the height of the gravel inside the cone. In which case we know what the lower limit for the height of the gravel will be, and the upper limit too (since we can have at most 8 metres of gravel in the cone, any more than that and it'd spill over).

That's a lot of assumptions about the question I'm making though, but either way the idea for deciding the domain for these kind of worded problems is the same, asking what values are realistic and what values are unrealistic.

Thanks for the reply! I took your advice and managed to do q1.
But still a little confused about the domain, i understand what you are getting at but not sure if my answer is 100%
-attached is the function displayed on graph
-if you cant read my writing roots are (0,0) (5,0), (6,0), MAX is (1.81, 96.77)

Now, my question concerns q1. d about the domain,
I believe the answer is either 0<x<5 or (0,5) U (6, 7.38] *as to where i got the 7.38 - its the value where the 2nd and last x value of the MAX
Another small question, if 0<x<5 were to be right, do I give the answer like this: 0<x<5 or this: (0, 5)

Thanks!

[Eugenet17]

bump.

for the second question, it asks to sketch the graph of V against h, showing the coordinates of all intercepts and the maximum turning point. Should i draw the entire graph or draw it with a limit of 0<h<8 even though it doesn't specifically ask to?

P.S the first question specifically states to sketch graph of V against x for suitable values of x.

[datfatcat]

bump.

for the second question, it asks to sketch the graph of V against h, showing the coordinates of all intercepts and the maximum turning point. Should i draw the entire graph or draw it with a limit of 0<h<8 even though it doesn't specifically ask to?

P.S the first question specifically states to sketch graph of V against x for suitable values of x.

For any "real life" situation, even if the question doesn't ask for domain, you need to put a restriction to make it realistic (sorry for the bad wordings haha).  For example, height cannot be negative nor can it go over the maximum point.  Same applies for many applications (such as no negative area, no negative temperature in K, negative rate of a person typing etc.)

[Eugenet17]

For any "real life" situation, even if the question doesn't ask for domain, you need to put a restriction to make it realistic (sorry for the bad wordings haha).  For example, height cannot be negative nor can it go over the maximum point.  Same applies for many applications (such as no negative area, no negative temperature in K, negative rate of a person typing etc.)

thats what i thought, thanks alot!