Given a 10 cm by 20 cm piece of paper, if you cut out four equal squares from the corners and fold up the resulting sides you will create an open box. Write an expression for the volume of this box in terms of the side length of each cut‐out square, x.
v = x(10-2x)(20-2x)
To find the expression for the volume of the box in terms of the side length of each cut-out square, let's break down the problem step by step:
1. Start with a 10 cm by 20 cm piece of paper.
2. Cut out equal squares from each corner of the paper. Since there are four corners, we will be cutting out four squares.
3. Let's assume the side length of each cut-out square is "x" cm.
4. After cutting out the squares, the paper will now have dimensions of (10 - 2x) cm by (20 - 2x) cm.
5. We can express the height of the resulting box as the side length of the cut-out squares, which is also "x" cm.
6. The volume of a box is given by the formula: volume = length × width × height.
7. Using the dimensions from step 4, the expression for the volume in terms of the side length of each cut-out square "x" would be: volume = (10 - 2x) cm × (20 - 2x) cm × x cm.
Therefore, the expression for the volume of the box in terms of the side length of each cut-out square, x, is:
volume = x(10 - 2x)(20 - 2x) cubic centimeters.