Final answer:
The volume V(x) of the open-top box made by cutting out squares of side length x from each corner of a 10 by 8 inches cardboard and folding up the sides is V(x) = (10 - 2x) * (8 - 2x) * x.
Step-by-step explanation:
To find a formula for the volume of the box formed from a piece of cardboard measuring 10 inches by 8 inches with squares of side length x cut out from each corner, we need to determine the dimensions of the box after the squares have been removed and the sides have been folded up.
The new length of the box will be (10 - 2x) inches, because we remove 'x' inches from both sides of the length. Similarly, the width will be (8 - 2x) inches. The height of the box will be x inches since that's the size of the squares we are cutting out from each corner.
The volume V(x) of a rectangular box is found by multiplying the length, width, and height together. Thus, the formula for the volume of the box in terms of x is:
V(x) = (10 - 2x) * (8 - 2x) * x