Question

A, B, C denote the areas of three coterminus 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 = A² + B² + C² 

(b) PS= AB + BC+ CA 

(c) P = S(A + B + C) 

(d) SP = (A + B + C)²

Answer 1

(b) PS= AB + BC+ CA

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

P = lbh, S = l + b + h, A = lh, B = lb, C = bh

PS = lbh (l + b + h) =

l²bh + lb²h + lbh² 

= (lb)(lh) + (lb)(bh) + (lh) (bh) 

= BA + BC + AC = AB + BC + CA