Question

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

Answer 1

(i)lateral surface area of cube is $4s^2=400c{m}^2$

lateral surface area of cuboid is $2h(l+w)=2.8(12.5+10)=360c{m}^2$

so cube has $40c{m}^2$ more area than cuboid

(ii)total surface area of cube is $6s^2=600c{m}^2$

total surface area of cuboid is $2(lw+wh+lh)=2(125+80+100)=610c{m}^2$

so cuboid has $10c{m}^2$ more area than cube