1. A square piece of cardboard measuring 60 inches on a side is made into a rectangular box by cutting identical squares from the four corners and then folding up the flaps. Let represent the length of the side of the discarded square. Write a formula for the volume of the box in terms of X.
Im so confused! Don't even know where to begin
Let x = side length of square discarded
The volume of rectangular solid is given by
V = lwh
where l, w and h are the length, width and height respectively.
When the flaps are folded up, it acquires a height, and this height measures x inches, since you cut a square with a side length of x inches.
The length and width are therefore decreased by 2x.
Thus, volume becomes
V = (60 - 2x)(60 - 2x)(x)
hope this helps~ `u`
No worries, I'm here to help! Let's break down the problem step-by-step.
1. Visualize the problem: Start by visualizing a square piece of cardboard that measures 60 inches on each side.
2. Cutting corners: Cut out identical squares from all four corners of the square piece of cardboard. The size of each cutout square is represented by "X".
3. Folding the flaps: Fold up the remaining flaps of the cardboard to form a rectangular box. The length and width of the box will be the dimensions of the cardboard after the squares are cut out.
4. Determine the length and width of the box: Since the length of the original square cardboard was 60 inches, cutting out squares from all four corners will reduce the overall length by 2X (X from each of the four corners). Similarly, the width of the box will be reduced by 2X as well.
Therefore, the length of the box will be (60 - 2X) inches, and the width of the box will also be (60 - 2X) inches.
5. Calculate the height of the box: The height of the box will be equal to the size of the cutout squares, which is "X" inches.
6. Formula for the volume: The formula for the volume of a rectangular box is length × width × height. Substituting the values, the formula for the volume of the box, in terms of "X", is:
Volume = (60 - 2X) × (60 - 2X) × X
Simplifying this expression will give you the final formula for the volume of the box in terms of "X".
Remember that this formula assumes the dimensions are in inches.