Question

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

Answer 1

$\left(i\right)$ Lateral surface area of cube

$=4$ (edge)${}^2$

$=4{\left(10\right)}^2=400$ cm${}^2$

Lateral surface area of cuboidal box

$=2(lh+bh)$
$=2(12.5\times 8+10\times 8)$

$=2\times 180=360$ cm${}^2$

$\therefore$ Lateral surface area of cubical box $>$ Lateral surface area of cuboidal box
$\Rightarrow$ Difference: $400-360$ cm${}^2$
$=40$ cm${}^2$

$\left(ii\right)$ Total surface area of cubical box

$=6$(edge)${}^2$
$={\left(6\right)}^2=300$ cm${}^2$

Total surface area of cuboidal box

$=2(lb+bh+lh)$
$=2(12.5\times 100+10\times 8+12.5\times 8)$
$=610$ cm${}^2$

Total S.A of cuboidal box $<$ cuboidal total S.A
Difference $=610-600{cm}^2=10$ cm${}^2$