A metal box measures `20 cm xx 12 cm xx 5 cm`. Thickness of the metal is 1 cm. Find the volume of the metal required to make the box.

Options

A. `550 cm^(3) `
B. `656 cm^(3) `
C. `660 cm^(3) `
D. `475 cm^(3) `

Answer

To find the volume of the metal required to make the box, we will follow these steps:

### Step 1: Calculate the volume of the outer box.
The dimensions of the outer box are given as:
- Length (L) = 20 cm
- Breadth (B) = 12 cm
- Height (H) = 5 cm

The formula for the volume of a cuboid is:
\[ \text{Volume} = L \times B \times H \]

Substituting the values:
\[ \text{Volume}_{\text{outer}} = 20 \, \text{cm} \times 12 \, \text{cm} \times 5 \, \text{cm} \]
\[ \text{Volume}_{\text{outer}} = 1200 \, \text{cm}^3 \]

### Step 2: Calculate the dimensions of the inner box.
Since the thickness of the metal is 1 cm, we need to subtract 2 cm from each dimension of the outer box (1 cm from each side).

- Inner Length (L') = 20 cm - 2 cm = 18 cm
- Inner Breadth (B') = 12 cm - 2 cm = 10 cm
- Inner Height (H') = 5 cm - 2 cm = 3 cm

### Step 3: Calculate the volume of the inner box.
Using the inner dimensions:
\[ \text{Volume}_{\text{inner}} = L' \times B' \times H' \]
\[ \text{Volume}_{\text{inner}} = 18 \, \text{cm} \times 10 \, \text{cm} \times 3 \, \text{cm} \]
\[ \text{Volume}_{\text{inner}} = 540 \, \text{cm}^3 \]

### Step 4: Calculate the volume of the metal required.
To find the volume of the metal used, we subtract the volume of the inner box from the volume of the outer box:
\[ \text{Volume}_{\text{metal}} = \text{Volume}_{\text{outer}} - \text{Volume}_{\text{inner}} \]
\[ \text{Volume}_{\text{metal}} = 1200 \, \text{cm}^3 - 540 \, \text{cm}^3 \]
\[ \text{Volume}_{\text{metal}} = 660 \, \text{cm}^3 \]

### Final Answer:
The volume of the metal required to make the box is **660 cm³**.

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