can you please solve it
Answers
Given :-
The dimensions of a iron piece are 40 cm × 12 cm × 80 cm.
It is melted into cubical pieces of side 4m each.
To find :-
Number of cubical pieces were made
Solution:-
Given that
The dimensions of a iron piece are 40 cm ×12 cm × 80 cm
We know that
Volume of a cuboid whose dimensions are l units , b units and h units is lbh cubic units
Volume of the iron piece = 40 × 12 × 80 cm³
=> Volume = 38400 cm³
Therefore,
The volume of the iron piece = 38400 cm³
The length of the side of the each cubical piece
= 4 m
We know that
1 m = 100 cm
4 m = 4×100 = 400 cm
We know that
The volume of a cube whose side is a units is a³ cubic units.
The volume of the cubical piece = (400)³ cm³
=> Volume = 400×400×400 = 64000000 cm³
The volume of each cubical piece
= 64000000 cm³
Let the number of cubical pieces were made be N
The volume of all N cubical pieces
= 64000000 N cm³
we know that
A solid is melted into another solid then The volume of the solid = The volume of the resultant solid
Therefore,
64000000 N = 38400
=> N = 38400/64000000
=> N = 0.0006
So , there is no chance to made cubical pieces from the given Iron piece .
Corrected Question:-
The dimensions of a iron piece are 40 cm × 12 cm × 80 cm.It is melted into cubical pieces of side 4 cm each.Find the number of pieces were made?
Solution:-
Given that
The dimensions of a iron piece are 40 cm ×12 cm × 80 cm
We know that
Volume of a cuboid whose dimensions are l units , b units and h units is lbh cubic units
Volume of the iron piece = 40 × 12 × 80 cm³
=> Volume = 38400 cm³
Therefore,
The volume of the iron piece = 38400 cm³
The length of the side of the each cubical piece
= 4 cm
We know that
The volume of a cube whose side is a units is a³ cubic units.
The volume of the cubical piece = 4³ cm³
The volume of each cubical piece
= 64 cm³
Let the number of cubical pieces were made be N
The volume of all N cubical pieces
= 64 N cm³
We know that
A solid is melted into another solid then The volume of the solid = The volume of the resultant solid
Therefore,
64 N = 38400
=> N = 38400/64
=> N = 600
So , Number of pieces = 600
Answer :-
The number of cubical pieces were made from the iron piece is 600
Used formulae:-
→The volume of a cube whose side is a units is a³ cubic units.
→ Volume of a cuboid whose dimensions are l units , b units and h units is lbh cubic units
Used Concept :-
→A solid is melted into another solid then The volume of the solid = The volume of the resultant solid