Question

$\text{The volume of a rectangular prism of base 4 m by 3 m is 60 m}{}^3\text{.}$
$\text{What will be the difference of its total surface area and lateral surface area?}$
$m^2$

Answer 1

We know that the prism has a base of $4$ m by $3$ m and a volume of $60$ m${}^3$.

Volume of the prism $=l\times b\times h$, where,
$l=$ Length, $b=$ Breadth, and $h=$ Height.

$\therefore 60=l\times b\times h$
$⟹60=4\times 3\times h$
$⟹60=12\times h$
$⟹h=\frac{60}{12}=5m$


Thus, Lateral Surface Area $=2(l+b)\times h$
$=2(4+3)\times 5$
$=2\times 7\times 5$
$=14\times 5=70$ m${}^2$


Total Surface Area $=2(lh+bh+lb)$
$=2(4\times 5+3\times 5+4\times 3)$
$=2(20+15+12)$
$=2\times 47=94$ m${}^2$

Therefore, their differences would be $94$ m${}^2$ - 70 m${}^2$ $=24$ m${}^2$

Alternatively, we can also say,
Total Surface Area $-$ Lateral Surface Area $=$ Sum of area of floor and ceiling
$=2\times (4\times 3)$
$=2\times 12=24$ m${}^2$