A closed metal box measure 30cm × 20cm × 10cm. thickness of the metal is 1cm. the volume of the metal required to make the box is:

Correct Answer: The correct option is 1968 cm³.

Step-by-step Explanation:

To find the volume of the metal required to make the closed box, we need to subtract the inner volume of the box from its outer volume.

1. Calculate the Outer Volume of the Box:

The external dimensions of the closed box are given as:

Outer Length ($L$) = 30 cm

Outer Breadth ($B$) = 20 cm

Outer Height ($H$) = 10 cm

The outer volume is calculated using the formula for the volume of a rectangular cuboid:

$V_{\text{outer}}=L\times B\times H$

$V_{\text{outer}}=30\times 20\times 10=6000{\text{cm}}^3$

2. Calculate the Inner Volume of the Box:

The thickness of the metal is 1 cm. Since the box is closed, metal adds to the thickness on both sides along length, breadth, and height.

Inner Length ($l$) = $30-2\times 1=28\text{cm}$

Inner Breadth ($b$) = $20-2\times 1=18\text{cm}$

Inner Height ($h$) = $10-2\times 1=8\text{cm}$

The inner volume is calculated as:

$V_{\text{inner}}=l\times b\times h$

$V_{\text{inner}}=28\times 18\times 8=4032{\text{cm}}^3$

3. Calculate the Volume of the Metal Required:

The volume of the metal is the difference between the outer volume and the inner volume:

$\text{Volume of metal}=V_{\text{outer}}-V_{\text{inner}}$

$\text{Volume of metal}=6000-4032=1968{\text{cm}}^3$

Thus, the volume of metal required to make the box is 1968 cm³.