Question

The outside measurements of a closed wooden box are 64 cm x 36 cm x 30 cm. If the thickness of the wood is 2.5 cm, what volume of wood is used to
make the box?​

Answer 1

Given:

The outer dimensions of the closed wooden box are:

Outer length = 64 cm

Outer breadth = 36 cm

Outer height = 30 cm

The thickness of the wood used is 2.5 cm

To find:

Volume of the wood used to make the box

Formula to be used:

$\boxed{Volume\: of\: a\: cuboid\: = length \:* \:breadth\: *\: height}$

Solution:

Since the thickness of the box is 2.5 cm

The inner dimensions of the wooden box will be:

Inner length = 64 - (2 × 2.5) = 64 - 5 = 59 cm

Inner breadth = 36 - (2 × 2.5) = 36 - 5 = 31 cm

Inner height = 30 - (2 × 2.5) = 30 - 5 = 25 cm

Therefore,

The outer volume of the closed box is,

= outer length × outer breadth × outer height

= 64 × 36 × 30

= 69,120 cm³

and

The inner volume of the closed box is,

= inner length × inner breadth × inner height

= 59 × 31 × 25

= 45,725 cm³

Now,

The volume of the wood will be,

= [outer volume of the closed box] - [inner volume of the closed box]

= [69120 cm³] - [45725 cm³]

= 23,395 cm³

Thus, the volume of wood used to make the box is 23,395 cm³.

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