Question

There are two cuboid boxes as shown in the adjoining figure. Which box requires the lesser amount of material to make.

Answer 1

Hint: Find the surface area of both the shapes, first shape is cuboid and second shape is cube. The surface region of a strong is the total of the regions of the plane or bended countenances of the strong. Surface zone of cuboid or 3D shape is the entirety of the surface regions of its six rectangular countenances.

Complete step-by-step solution -
It is estimated in square units, for example, square centimeter \[(c{{m}^{2}})\] and square meter (\[{{m}^{2}}\]).
For Box 1:
     Length \[=l=60\,cm\]
     Breadth \[=b=40\,cm\]
     Height\[=h=50\,cm\]
Total surface area of cuboid box
     \[2\left( lb+bh+hl \right)\]
     \[=2\left( 60\times 40+40\times 50+50\times 60 \right)\]
     \[=2\times \left( 2400+2000+3000 \right)\]
     \[=2\times 7400\]
     \[=14800\,c{{m}^{2}}\]
For Box 2: side = \[50\,cm\]
     Total surface area of cube shape box \[=6\times {{\left( side \right)}^{2}}\]
                              \[=6\times {{\left( 50 \right)}^{2}}\]
                              \[=6\times 2500\]
                              \[=15000\,c{{m}^{2}}\]
So, the cube has more surface area than the cuboid box. Box 1 requires a lesser amount of material to make.
Difference between cuboid and cube: The key distinction among cube and cuboid is: cube is a solid shape which has six square-formed countenances of a similar size yet a cuboid has rectangular appearances. Although both 3D shapes appear to be identical in structure they have a couple of various properties dependent on anxious length, diagonals and countenances.
In Geometry, there are numerous shapes, for example, chamber, circle and cone that have unmistakable properties yet just cuboid and block are two such solids which have some basic properties like both eight vertices and twelve edges. Likewise, all the inside edges are equivalent to 90 degrees.

Note: Clear the concept of $2D$ and $3D$ shapes. Shapes are very important in math specially in geometry. One should go through the properties of shapes. Each shape has its identity. The total surface area of the box is lesser than the total surface area of the box. By surface zone of a cube or cuboid which has been evaluated in the all-out surface territory.