A box with lid is made of 2 cm thick wood. Its external length, breadth and height are 25 cm, 18 cm and 15 cm respectively. How much cubic cm of liquid can be places in it> Also, find the volume of the wood used in it.
Answers
Answer:
Step-by-step explanation:
volume of cuboid = l * h * w
∴volume of box from out side
= 25*18*15
=6750 cm²
now box from inside
=(25-2)*(18-2)*(15-2)
=4784
∴4784 cubic cm of liquid can be place in it
and volume of wood used is
6750-4784
=1966 cm²
4784 cubic cm (cm³) of liquid can be placed in the wooden box.
The volume of wood used in making the box is 1966 cm³.
• Given,
External length of the box (l) = 25 cm
External breadth of the box (b) = 18 cm
External height of the box (h) = 15 cm
∴ External volume of the box = l × b × h
= 25 cm × 18 cm × 15 cm
= 6750 cm³
• Now, given that,
Thickness of the wood used in making the box = 2 cm
∴ Internal length of the box = External length - Thickness of the wood
=> Internal length = 25 cm - 2cm = 23 cm
Internal breadth of the box = External breadth - Thickness of the wood
=> Internal breadth = 18 cm - 2 cm
= 16 cm
Internal height of the box = External height - Thickness of the wood
=> Internal height = 15 cm - 2 cm = 13 cm
• Therefore, internal volume of the box = Internal length × Internal breadth × Internal height
Or, Internal Volume = 23 cm × 16 cm × 13 cm = 4784 cm³
• Therefore, volume of liquid that the box can accomodate = Internal volume of the box
=> Volume of liquid that can be filled in the box = 4784 cm³
• Volume of wood used in making the box = External volume of the box - Internal volume of the box
Or, Volume of wood used in the box = 6750 cm³ - 4784 cm³
= 1966 cm³