At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
the answer the book gave was S(x)= x^2 + (8/x), x>0 but I don't understand this
Start with the base of the box. You know its area is length x width, and that since its a square, the length of the each side of the base are equal to each other. So you can say length x length = the are of the base. Now each side of the box has the area length x height. Notice that "length" here means the same as the "length" on the base, because they are connected to the base :D. Think about this, try drawing a picture and make a formula for it. The last bit is just considering how it relates to the 2m^3 volume you've been given, but I think that depends on the level of maths you are in.
but how do you find surface area?
Sorry, working on my own homework. Im not sure I understand your question. The area of a 2d object is its surface area.
Can you express the volume of the box using the figure above?
@mangoes20 Are you still there?
i'm just not understanding at alll
Do you see my figure above?
If you want help with this problem, I'll help you now. If you don't answer, I'm getting off in a few minutes.
ok i'm ready
OK, Look at the figure above. That is a box with a base and 4 sides but no top.
The surface area of the box is the sum of the areas of all 4 vertical faces and the area of the base.
The base of the box is a square with side length x. What is the area of the base?
x x y
No. That is the volume of the box which we'll need soon. The base of the box is a square. The area of a square is the square of the side. Since the side of the base has length x, the area of the base is x^2.
Now we have the area of the base. The next thing we need is the area of the 4 vertical sides. Each vertical side is a rectangle with side lengths x and y. What is the area of each vertical side?
How do you get xy^2 from multiplying x and y? Each side is a rectangle x by y, so its area is simply xy.
There are 4 vertical sides, so the total are of vertical sides is 4xy.
Now we have the area of the base is x^2, and the area of all 4 sides is 4xy. A = x^2 + 4xy
We need the area expressed in terms of x only, but we have y in the expression. Now we use the volume to get rid of y.
The volume of a box is V = LWH ( volume = length * width * height)
For this box, we are given the volume is 2 m^3. The volume is V = x * x* y V = x^2y
We are given that the volume is 2 m^2, so we write x^2y = 2, and we solve for y: y = 2/(x^2)
Now we go back to our expression for the area, and we replace y with 2/(x^2): A = x^2 + 4xy A = x^2 + 4x[2/(x^2)] A = x^2 + 8x/x^2 A = x^2 + 8/x
wow you actually made that make sense!
That's great. Go over it step by step. It's important to learn the method.
Oh I will