Question

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

Answer 1

Hint: In this type of the question this is important to learn all formulas of the surface area, cuboid and cube etc. We have to know how to identify the cube and cuboid by its side or corners. Both are cuboid so, we just need the formula of the surface area of the cuboid .

Complete step-by-step answer:
Mensuration is the surface of the branch of mathematics which concerns itself with the measurement of lengths, area & volume of the plane or curved faces of the solid.
Surface area of a solid is the sum of the areas of the plane or curved faces of the solid. Surface of the area is only measured in square centimeters and square meters.
Here we use the formula of surface area of cuboid which is $2(lb + lh + bh)$
Here l stands for length, b for breadth and h for the height of the cuboid.
$l = 60cm, b = 40cm, h = 50cm$
The surface area of the cuboid first
$ = 2(60.40 + 40.50 + 60.50) $
$ = 2(2400 + 2000 + 3000) $
$ = 2.7400$
$ = 14800c{m^2} $
Now we have the surface area of cuboid is $14800c{m^2} $
The surface area of second cuboid is
$2(lb + lh + bh) $
Where $l = 50cm, b = 50cm, h = 50cm$
Surface area $ = 2(50.50 + 50.50 + 50.50) $
$ = 2(2500 + 2500 + 2500) $
$ = 2.7500$
$ = 15000c{m^2} $
So, the surface area of the second cuboid is $15000c{m^2} $
Surface area of first cuboid < Surface area of second cuboid

Hence, the cuboidal box first requires the lesser amount of material to make, since the surface area of the first box is less that of the second box.

Note: Here in this question we can clearly see that the second cuboid has all the three-side equal which means it is cube in shape. We can find the surface area of the second shape by the formula of surface area of the cube.
Surface area of cube $ = 6.a. a$
$ = 6.50.50$
$ = 6.2500$
$ = 15000c{m^2}$