The dimension of an open box are 52 cms, 40 cms and 26 cms. Its thickness is 1 cm. If 1 cubic cm of the metal used in the box weights 1 gm, then he weight of the box is

Options

A. `8 cdot 48` kg
B. `6 cdot 58` kg
C. `7 cdot 28` kg
D. 658 gms

Answer

To find the weight of the open box, we will follow these steps:

### Step 1: Calculate the outer dimensions of the box.
The outer dimensions of the box are given as:
- Length = 52 cm
- Breadth = 40 cm
- Height = 26 cm

### Step 2: Calculate the inner dimensions of the box.
Since the thickness of the box is 1 cm, we need to subtract twice the thickness (1 cm from each side) from each dimension to get the inner dimensions:
- Inner Length = 52 cm - 2(1 cm) = 50 cm
- Inner Breadth = 40 cm - 2(1 cm) = 38 cm
- Inner Height = 26 cm - 2(1 cm) = 24 cm

### Step 3: Calculate the volume of the outer box.
The volume of the outer box can be calculated using the formula for the volume of a rectangular prism:
\[ \text{Volume}_{\text{outer}} = \text{Length} \times \text{Breadth} \times \text{Height} \]
\[ \text{Volume}_{\text{outer}} = 52 \, \text{cm} \times 40 \, \text{cm} \times 26 \, \text{cm} \]
\[ \text{Volume}_{\text{outer}} = 54080 \, \text{cm}^3 \]

### Step 4: Calculate the volume of the inner box.
Using the same formula for the inner box:
\[ \text{Volume}_{\text{inner}} = \text{Inner Length} \times \text{Inner Breadth} \times \text{Inner Height} \]
\[ \text{Volume}_{\text{inner}} = 50 \, \text{cm} \times 38 \, \text{cm} \times 24 \, \text{cm} \]
\[ \text{Volume}_{\text{inner}} = 45600 \, \text{cm}^3 \]

### Step 5: Calculate the volume of the metal used in the box.
The volume of the metal used is the difference between the outer volume and the inner volume:
\[ \text{Volume}_{\text{metal}} = \text{Volume}_{\text{outer}} - \text{Volume}_{\text{inner}} \]
\[ \text{Volume}_{\text{metal}} = 54080 \, \text{cm}^3 - 45600 \, \text{cm}^3 \]
\[ \text{Volume}_{\text{metal}} = 8480 \, \text{cm}^3 \]

### Step 6: Calculate the weight of the box.
Given that 1 cubic cm of metal weighs 1 gram, the weight of the box can be calculated as:
\[ \text{Weight} = \text{Volume}_{\text{metal}} \times 1 \, \text{gram/cm}^3 \]
\[ \text{Weight} = 8480 \, \text{grams} \]

### Step 7: Convert the weight into kilograms.
To convert grams to kilograms, divide by 1000:
\[ \text{Weight in kg} = \frac{8480 \, \text{grams}}{1000} = 8.48 \, \text{kg} \]

Thus, the weight of the box is **8.48 kg**.

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