Suppose you take a piece of cardboard measuring 7 inches by 7 inches, cut out square corners with sides x inches long, and then fold up the cardboard to make an open box. Express the volume V of the box as a function of x.
I knew this question sounded familiar.
I answered it two days ago.
http://www.jiskha.com/display.cgi?id=1245803469
PLEASE ANSWER
To express the volume V of the box as a function of x, we need to determine the dimensions of the box.
Let's go step by step:
1. Start with a piece of cardboard measuring 7 inches by 7 inches.
2. Cut out square corners with sides x inches long.
After cutting out the square corners, the remaining dimensions of the cardboard will be:
Length: 7 inches - 2x inches (as both sides have been reduced by x inches)
Width: 7 inches - 2x inches (same reasoning as length)
3. Fold up the cardboard to make an open box.
By folding along the edges, we create the height of the box, which is equal to x inches.
So, the dimensions of the box are:
Length: 7 inches - 2x inches
Width: 7 inches - 2x inches
Height: x inches
4. Calculate the volume of the box.
The volume V of a rectangular box is given by the formula: V = Length * Width * Height.
In our case:
V = (7 - 2x) * (7 - 2x) * x
Simplifying, we get:
V = (49 - 14x + 4x^2) * x
Therefore, the volume V of the box is expressed as a function of x: V(x) = 4x^3 - 14x^2 + 49x.
The link shows something like the box described in the question. Disregard the cover.
(Broken Link Removed)
Width of the box = 7-x-x = 7-2x
Length of the box = 7-x-x = 7-2x
Height of the box = x
Can you calculate the volume?