Question

There are two cuboidal boxes as shown in the adjoining figure.

Which box requires the lesser amount of material to make?

Answer 1

Step-1: Find the total surface area of$boxa$ as shown in the figure.

The total surface area of$boxa$$=2\times (l\times b+b\times h+h\times l)$ (As $boxa$is in cuboidal shape )

Length, $l=60cm$

breadth, $b=40cm$ ( As per the given $boxa$diagram )

Height, $h=50cm$

The total surface area of$boxa$$=2\times (60\times 40+40\times 50+50\times 60)$

The total surface area of$boxa$$=2\times (2400+2000+3000)$

The total surface area of$boxa$$=2\times 7400$

The total surface area of$boxa$$=14,800c{m}^2$--------- (i)

Step-2: Find the total surface area of$boxb$ as shown in the figure.

The total surface area of$boxb$$=6\times {\left(side\right)}^2$ (As $boxb$is in cubical shape )

Side, $s=50cm$ ( As per the given $boxb$diagram )

The total surface area of$boxb$$=6\times {\left(50\right)}^2$

The total surface area of$boxb$$=6\times 2500$

The total surface area of$boxb$$=15,000c{m}^2$--------- (ii)

From (i) and (ii), we can clearly see that total surface area of $boxa$is lesser than $boxb$

Hence, $boxa$requires a lesser amount of material to make it.