Final answer:
The volume of the open-topped box can be found by first solving for the size of the square cut from each corner, denoted as x, using the base area equation (50 - 2x)(40 - 2x) = 875 cm2, and then calculating the volume using the formula 875 cm2 × x cm.
Step-by-step explanation:
We are asked to determine the volume of an open-topped box made from a 50 cm by 40 cm rectangle, from which equal squares are cut from each corner and the resulting flaps are folded up to form the sides of the box. The base area of the box is specified to be 875 cm2.
Let's denote the side of the square cut from each corner as x cm. After cutting and folding, the length and width of the base of the box become (50 - 2x) cm and (40 - 2x) cm respectively. To find the value of x, we set up the equation for the base area:
(50 - 2x)(40 - 2x) = 875
Solving this quadratic equation will give us the value of x. Once x is known, the height of the box, which is also x because it's the size of the cut-out square, can be used to calculate the volume. Therefore, the volume of the box is given by:
Volume = base area × height = 875 cm2 × x cm
After calculating the correct value for x, we would substitute it back into the volume formula to find the box's volume.