Question

find the volume of wood used to make a closed rectangular box of outer dimensions 60 cm ×45 cm × 32 CM the thickness of wood being 2.5 CM all around. also find the capacity of the box.​

Answer 1

Answer:

Volume of wood used = 27000 cm³

Capacity of the box = 59400 cm³

Solution:

⇒ Given:

Length of box = 60 cm

Breadth of the box = 45 cm

Height of the box = 32 cm

Thickness of the wood = 2.5 cm

First of all we can find the total volume of the given box.

Formula:

$\sf{\boxed{Volume\:of\:cuboid=lbh}}$

Substituting the required values in the equation:

Volume of the cuboid = 60 x 45 x 32

= 86400 cm³

Now, we will find the capacity of the box, that is the amount of matter that can be stored in it. For this, we first need to find the actual length, breadth and height of the box excluding the thickness of the wood.

Length = 60 - (2.5 x 2) = 55 cm

Breadth = 45 - (2.5 x 2) = 40 cm

Height = 32 - (2.5 x 2) = 27 cm

Formula:

$\sf{\boxed{Volume\:of\:cuboid=lbh}}$

Substituting the values in the equation:

Capacity = 55 x 40 x 27

= 59400 cm³

At last, we need to find the volume of wood used. For this we need to subtract the capacity of the box from the total volume.

Formula:

$\sf{\boxed{Volume\:of\:wood=Total\:volume-Capacity}}$

Substituting the values in the equation:

Volume of wood = 86400 - 59400

= 27000 cm³