Question

$A,B,C$ denote the areas of three co-terminus faces of a cuboid. If $P$ and $S$ denote the product and sum of dimensions of the cuboid respectively, which one of the following is correct?

• A. $PS=A^2+B^2+C^2$
• B. $PS=AB+BC+CA$
• C. $P=S(A+B+C)$
• D. $SP=(A+B+C){}^2$

Answer 1

The correct option is B $PS=AB+BC+CA$

Let $l,b$ and $h$ be the length, breadth and height of the cuboid respectively.

Given, $P=lhb,S=l+b+h,A=lh,B=lb,C=bh$
Now, $PS=lbh\times (l+b+h)$

$=l^{2}bh+l{b}^{2}h+lb{h}^2$

$=B\times A+B\times C+A\times C$

$=AB+BC+AC$