Question

An open box is constructed with a rectangular sheet of metal 10 cm x 14 cm and cutting a
square of side x cm from each corner. The resulting projections are folded up and the
streams welded. Show that the volume of the resulting box is (140x - 48x + 4x) cm.​

Answer 1

Answer:

See the diagram green area is base of our box whose area is (10-2x)×(14-2x) and height x so volume

$v = (10-2x)×(14-2x) \times x \\ \: \: \: = x(4 {x}^{2} - 48x + 140) \\ \: \: \: = 4 {x}^{3} - 48 {x}^{2} + 140x</p><p>$