Question

The total surface area of a box which is in the form of a cuboid whose dimensions are $l\times b\times h$ is _______.

• A. $2(lb+bh+hl)$
• B. $(lb+bh+hl)$
• C. $2(lh+bh)$
• D. $(lh+bh)$

Answer 1

Answer: (A)

The total surface area of a cuboid is nothing but the sum of the area of six rectangular regions forming the cuboid.

Clearly, Cuboid is bounded by six rectangular faces.

It is given that, the dimensions of cuboid are $l\times b\times h$

From figure,

T.S.A of cuboid $=ar\left(ABCD\right)+ar\left(CEFD\right)+ar\left(EFGH\right)+ar\left(ABHG\right)+ar\left(BCEH\right)+ar\left(ADFG\right)$

$=(l\times h)+(b\times h)+(l\times h)+(b\times h)+(l\times b)+(l\times b)$

$=lh+bl+lh+bh+lb+lb$

$=2(lb+bh+lh)$

Total surface area of cuboid is $2(lb+bh+lh)$.

Hence, Option $A$ is correct.