Squares, each of side 6 cm are cut off from the four corners of a sheet of tin measuring 42 cm by 30 cm. The remaining portion of the tin sheet is made into an open box by folding up the flaps . Find the capacity of the box formed.

Answer

To find the capacity of the open box formed by cutting squares from the corners of a tin sheet and folding up the flaps, we can follow these steps:

### Step 1: Determine the dimensions of the original tin sheet.
The original dimensions of the tin sheet are given as:
- Length = 42 cm
- Width = 30 cm

### Step 2: Calculate the dimensions of the box after cutting the corners.
Since squares of side 6 cm are cut from each corner, we need to adjust the dimensions of the tin sheet accordingly.

- **New Length (L)**:
\[ L = \text{Original Length} - 2 \times \text{Side of Square} = 42 \, \text{cm} - 2 \times 6 \, \text{cm} = 42 \, \text{cm} - 12 \, \text{cm} = 30 \, \text{cm} \]

- **New Width (W)**:
\[ W = \text{Original Width} - 2 \times \text{Side of Square} = 30 \, \text{cm} - 2 \times 6 \, \text{cm} = 30 \, \text{cm} - 12 \, \text{cm} = 18 \, \text{cm} \]

### Step 3: Determine the height of the box.
The height of the box is equal to the side of the squares cut from the corners, which is:
- Height (H) = 6 cm

### Step 4: Calculate the volume (capacity) of the box.
The volume of a rectangular box is given by the formula:
\[ \text{Volume} = \text{Length} \times \text{Width} \times \text{Height} \]
Substituting the values we found:
\[ \text{Volume} = 30 \, \text{cm} \times 18 \, \text{cm} \times 6 \, \text{cm} \]

Calculating the volume:
\[ \text{Volume} = 30 \times 18 \times 6 = 3240 \, \text{cm}^3 \]

### Final Answer:
The capacity of the box formed is **3240 cm³**.

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