The volume of the cuboid is given by V = yx². The equation for the total length of all the edges is 4x + 2y = 112. By substituting the value of y into the volume equation, we get V = 28x² - 2x³.
To find the volume of the cuboid, we multiply the length, width, and height together. Since the width and height are both x cm, the volume is given by V = y * x * x = yx².
The total length of all the edges of the cuboid can be found by adding up all the edges. Each edge has a length of y cm or x cm, so the total length is 2(x + y + x + y) = 4x + 2y. We are given that this total length is 112 cm. Therefore, we can write the equation 4x + 2y = 112.
Solving this equation for y, we get y = 56 - 2x.
Substituting this value of y into the volume equation, we get V = (56 - 2x)x² = 56x² - 2x³.
Therefore, we have shown that V = 28x² - 2x³.
Below is the diagram of the question.