Question

A person wants to make an open box by cutting equal squares from the corners of apiece of metal 160cm by 240cm as shown .if the edge of each cut out square is x cm find the volume of the box ,when x=1and x=3

Answer 1

To find the volume of the open box, calculate the volume of the rectangular base and then multiply it by the height. The length and width of the rectangular base are (160 - 2x) cm and (240 - 2x) cm, respectively. The volume of the box when x = 1 is 158 * 238 * h, and when x = 3 it is 154 * 234 * h.

Step-by-step explanation:

To find the volume of the open box, we need to calculate the volume of the rectangular base and then multiply it by the height. The rectangular base is formed by the length and width of the metal minus the length of the cut-out squares on each side.

The length and width of the rectangular base would be (160 - 2x) cm and (240 - 2x) cm, respectively. The height of the box can be any value we choose. Therefore, the volume of the open box is given by (160 - 2x) * (240 - 2x) * h.

If we substitute x = 1 into the volume formula, we get (160 - 2*1) * (240 - 2*1) * h = 158 * 238 * h. Similarly, if we substitute x = 3, we get (160 - 2*3) * (240 - 2*3) * h = 154 * 234 * h.

So, when x = 1, the volume of the box is 158 * 238 * h, and when x = 3, the volume of the box is 154 * 234 * h.