Question

A cubical box has each edge $10$cm and another cuboidal box is $12.5$cm long,$10$cm wide and $8$ cm high. Which box has the smaller total surface area and by how much?

Answer 1

A cuboid box and a cuboidal box

edge of cube $=10$cm

Length (l) of box $=12.5$cm

Breadth (b) of box $=10$cm

Height (h) of box $=8$cm

Total surface area of cubical box

$=6(a{)}^2$

$=6(100{)}^2$

$=6\times \left(100\right)$

$=600c{m}^2$

Total surface area of cuboidal box

$=2[lh+bh+bl]$

$=2[12.5\times 8+10\times 8+10\times 12.5{]}^{3}c{m}^2$

$=2(100+80+125)c{m}^2$

$=2\left(305\right)c{m}^2$

$=610c{m}^2$

So, Total surface area of cubical box $<$ total surface area of cuboidal box.

Total surface area of cuboidal box $-$ Total surface area of cubical box

$=610c{m}^2-600c{m}^2$

$=10c{m}^2$

Therefore,

Total surface area of the cuboidal box is smaller than the total surface area of the cuboidal box by $10c{m}^2$.