Question

The volume of a rectangular prism of base 4 meters by 3 meters is 60 cubic meters. What will the difference between its total surface area and lateral surface area be?

• A. 18 sq m
  
• B. 24 sq m
  
• C. 16 sq m
  
• D. 21 sq m
  

Answer 1

The correct option is B 24 sq m


We know that the prism has a base of 4 m by 3 m, and a volume of 60 cu m.

Volume of the prism $=l\times b\times h$, where l = length, b = width, and h = height.

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

Thus, the lateral surface area $=2(l+b)\times h$
$=2(4+3)\times 5$
$=2\times 7\times 5=70$ sq m

Total surface area $=2(lb+bh+hl)$
$=2(4\times 3+3\times 5+5\times 4)$
$=2(12+15+20)$
$=2\times 47=94$ sq m

Therefore, the required difference $=94-70=24$ sq m.