Question

A cubical box has each edge 10$cm$ and another cuboidal box is $12.5cm$ long, 10$cm$ 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

The dimensions of first box is $l=10;b=10;h=8$

The dimensions of second box is $l=12.5;b=10;h=8$

$i)$ Lateral surface area of first box $2h(l+b)2\left(8\right)(10+10)16\left(20\right)320c{m}^2$

Lateral surface area of second box $2h(l+b)2\left(8\right)(12.5+10)16\left(22.5\right)360c{m}^2$

So the lateral surface area of second box is greater by $360-320=40c{m}^2$

$ii)$ Total surface area of first box is given by $2(lb+bh+hl)2\left(\right(10\left)\right(10)+(10\left)\right(8)+(10\left)\right(8\left)2\right(100+80+80\left)2\right(260)520c{m}^2$

Total surface area of Second box is given by $2(lb+bh+hl)2\left(\right(12.5\left)\right(10)+12.5(8)+10(8\left)2\right(125+100+80\left)2\right(305)610c{m}^2$

The Total surface area of first box is smaller by $610-520=90c{m}^2$