# Thread: Maths Assignment Help !

1. ## Maths Assignment Help !

Could someone please help me with this question, I really have know clue how to do this.

A parcel is to be tied with a length of string in a normal way.

Assume that the parcel is a cuboid with square cross section and with a volume (V) of 16000 cm^3. Find an expression for the length of string, L(x), in terms of the side of the square cross section, x

And..

determine the dimensions of the parcel that will minimize the length of string required.

Any help would be greatly appreciated.

2. ## Re: Maths Assignment Help !

Originally Posted by PapaJones
Could someone please help me with this question, I really have know clue how to do this.

A parcel is to be tied with a length of string in a normal(?) way.

Assume that the parcel is a cuboid with square cross section and with a volume (V) of 16000 cm^3. Find an expression for the length of string, L(x), in terms of the side of the square cross section, x

And..

determine the dimensions of the parcel that will minimize the length of string required.

Any help would be greatly appreciated.
1. Use $V_{cuboid}= \text{base-area} \cdot \text{height}$

With your values: $V = x^2 \cdot h~\implies~h=\frac{16000}{x^2}$

2. The length of the string consists of the circumferences of the cross-sections (I hope that this is meant by "the normal way" you mentioned). Two of the three cross-sections are equal due to the quadratic base area:

$L(x)= 4x + (2x+2h)+(2x+2h)=8x + \frac{4 \cdot 16000}{x^2}$

3. To minimize L differentiate L wrt x and solve L'(x) = 0 for x. You should come out with a cube.

3. ## Re: Maths Assignment Help !

Sorry, by "normal" I meant that the string goes all the way around the parcel including underneath it. Is the answer still the same?

4. ## Re: Maths Assignment Help !

Originally Posted by PapaJones
Sorry, by "normal" I meant that the string goes all the way around the parcel including underneath it. Is the answer still the same?
I've attached a sketch to show you what I believe is a normal way to tie up a parcel. (The red lines indicate the string)

... and I used this sketch to do my calculations.

5. ## Re: Maths Assignment Help !

Thats correct for my question, except the string around the sides that doesn't go underneath the parcel. Only 2 strings in my question.

6. ## Re: Maths Assignment Help !

Originally Posted by PapaJones
Thats correct for my question, except the string around the sides that doesn't go underneath the parcel. Only 2 strings in my question.
then modify what earboth has provided as a solution path ... you should be able to come up with a suitable equation on your own to minimize.