A rectangular sheet of metal is 40 cm by 15 cm. Equal squares of side 4 cm are cut off at the corners and the remainder is folded up to form an open rectangular box. The volume of the box is

Options

A. a)`896 cm^(3)`
B. b)`986 cm^(3)`
C. c)`600 cm^(3)`
D. d)`916 cm^(3)`

Answer

To find the volume of the open rectangular box formed by folding up the corners of the rectangular sheet of metal, we will follow these steps:

### Step 1: Understand the dimensions of the original sheet
The original rectangular sheet has a length of 40 cm and a width of 15 cm.

### Step 2: Determine the dimensions after cutting squares
Equal squares of side 4 cm are cut off from each corner. This means:
- The length of the sheet will be reduced by 4 cm from each end, totaling 8 cm (4 cm from each end).
- The width of the sheet will also be reduced by 4 cm from each end, totaling 8 cm.

Thus, the new dimensions after cutting the squares are:
- New length = 40 cm - 8 cm = 32 cm
- New width = 15 cm - 8 cm = 7 cm

### Step 3: Determine the height of the box
The height of the box will be equal to the side of the squares cut out, which is 4 cm.

### Step 4: Calculate the volume of the box
The volume \( V \) of a rectangular box is given by the formula:
\[ V = \text{length} \times \text{width} \times \text{height} \]

Substituting the values we found:
\[ V = 32 \, \text{cm} \times 7 \, \text{cm} \times 4 \, \text{cm} \]

### Step 5: Perform the multiplication
Calculating the volume:
1. First, calculate \( 32 \times 7 = 224 \, \text{cm}^2 \)
2. Now multiply by the height: \( 224 \times 4 = 896 \, \text{cm}^3 \)

Thus, the volume of the open rectangular box is **896 cm³**.

### Summary of the solution:
The volume of the box formed by folding up the corners is **896 cm³**.

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