How many boxes, each of size 2 m x 3 m x 4 m, can be packed in a carton of size 12 m x 24 m x 44 m?
Answers
72 boxes each of size 2 m x 3 m x 4 m, can be packed in a carton of size 12 m x 24 m x 44 m
Step-by-step explanation:
GIVEN SIZE
2 m x 3 m x 4 m
___________________________
TO FIND
How many boxes, each of size 2 m x 3 m x 4 m, can be packed in a carton of size 12 m x 24 m x 44 m
___________________________
Area Of Boxes
We know that,
Area Of Cuboid = 2 × [ ( Length × Breadth ) + ( Breadth × Height ) + ( Height × Length ) ]
Here,
Length = 2 m
Breadth = 3 m
Height = 4 m
We know that,
Area Of Cuboid = 2 × [ ( Length × Breadth ) + ( Breadth × Height ) + ( Height × Length ) ]
Area Of Cuboid = 2 × [ ( 2 × 3 ) + ( 3 × 4 ) + ( 4 × 2 ) ]
Area Of Cuboid = 2 × ( 6 + 12 + 8 )
Area Of Cuboid = 2 × 26
Area Of Cuboid = 52
Area Of Cuboid = 52 cm²
Area Of Boxes = 52 cm²
___________________________
Area Of Carton
We know that,
Area Of Cuboid = 2 × [ ( Length × Breadth ) + ( Breadth × Height ) + ( Height × Length ) ]
Here,
Length = 12 m
Breadth = 24 m
Height = 44 m
We know that,
Area Of Cuboid = 2 × [ ( Length × Breadth ) + ( Breadth × Height ) + ( Height × Length ) ]
Area Of Cuboid = 2 × [ ( 12 × 24 ) + ( 24 × 44 ) + ( 44 × 12 ) ]
Area Of Cuboid = 2 × ( 288 + 1056 + 528 )
Area Of Cuboid = 2 × 1872
Area Of Cuboid = 3744
Area Of Cuboid = 3744 cm²
Area Of Carton = 3744 cm²
___________________________
We know that,
Number Of Boxes = Area Of Carton / Area Of Boxes
Number Of Boxes = 3744 / 52
Number Of Boxes = 72