A box with a lid is made of wood which is 3 cm thick. Its external length, breadth and height are 56 cm, 39 cm and 30 cm respectively. Find the capacity of the box. Also find the volume of wood used to make the box.
Given that,
External length = 56 cm
External width = 39 cm
External height = 30 cm
We know that,
Volume of cuboid = Length × Breadth × Height
Therefore,
External volume of the box = 56 × 39 × 30
= 65520 cm3
It is also given that,
Thickness of the wood = 3 cm
Therefore,
Internal length = 56 – (3 × 2) = 50 cm
Internal width = 39 – (3 × 2) = 33 cm
Internal height = 30 – (3 × 2) = 24 cm
As we know that,
Volume of cuboid = Length × Breadth × Height
Therefore,
Capacity of box = Internal volume of the box = 55 × 40 × 27
= 39600 cm3
Hence,
Volume of wood = External volume – Internal volume
= 65520 – 39600
= 25920 cm3