Math Is Fun Forum

Saitenji

Member

Registered: 2005-09-24

Posts: 10

Word Problems (Precalculus)

Well, I'm having trouble with this problem mostly because I'm not quite sure what it's asking for...Because of that, I am unable to do part a), which asks for a function.

Functions and Their Graphs

An open box with a square base is required to have a volume of 10 cubic feet.

a) Express the amount A of material used to make such a box as a function of the length x of a side of the square base.

b) How much material is required for a base 1 foot by 1 foot?

c) How much material is required for a base 2 feet by 2 feet?

d) Graph A = A(x). For what value of x is A smallest?

Any help would be very much appreciated. Hope to hear from you guys soon!

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Word Problems (Precalculus)

a)

You need to find a function for the amount of material you need to use to make the box. The box is open, so it will have one square base and 4 rectangular sides. The sides of the square are both x, and the rectangles have a width of x and a length of 10/x², so that the volume is always 10 cubic feet.

Therefore, A = x² + 4(x * 10/x²) = x² + 40/x.

b) and c) are just substituting values of x into the equation you just made.
For b), x = 1 and so A = 1² + 40/1 = 41 square feet.
For c), x = 2 and so A = 2² + 40/2 = 24 square feet.

d) Needs you to find the value of x that makes A smallest.
The question states that you must draw a graph to do this. So, all you do is draw the graph of A = x² + 40/x and then read the values of x and A where A is smallest.

---

Why did the vector cross the road?
It wanted to be normal.

Saitenji

Member

Registered: 2005-09-24

Posts: 10

Re: Word Problems (Precalculus)

Thanks a bunch!
At first, I was just really confused...I mean, I didn't quite understand what the problem was asking for...But thanks to you, it's all so clear now; I can't believe I couldn't figure it out!

Thanks again.