A rectangular sheet of metal is 60 cm by 25 cm. Equal squares of side 5 cm are cut off at the corners and the remainder is folded up to form an open rectangular box. Find the volume of the box.

The correct option is 3750 cm³.

To find the volume of the open rectangular box, we need to determine its dimensions (length, width, and height) after folding the remainder of the metal sheet.

Step 1: Understand the dimensions of the original sheet
The rectangular sheet of metal initially measures 60 cm by 25 cm.

Step 2: Determine the dimensions of the box after cutting and folding
Equal squares of side 5 cm are cut off at the four corners. When the sides are folded up, this height of the fold becomes the height of the box, and the length and width of the base are reduced from both ends by the side length of the square:
- Height ($h$) of the box = 5 cm
- Length ($l$) of the box = $60-2\left(5\right)$
- Width ($w$) of the box = $25-2\left(5\right)$

Calculating the length and width:

$l=60-10=50\text{cm}$

$w=25-10=15\text{cm}$

Step 3: Calculate the volume of the box
The formula for the volume ($V$) of a rectangular box is:

$V=l\times w\times h$

Substituting the values of length, width, and height into the formula:

$V=50\times 15\times 5$

$V=750\times 5=3750{\text{cm}}^3$

Thus, the volume of the box is 3750 cm³.