Formula

Volume and wall area of a cuboid

Mensuration • Solids • Cuboid

Formula

V = l bh, four walls = 2 (l + b) h

A cuboid of length

l

, breadth

b

and height

h

has volume

l bh

, lateral surface (the four walls)

2 (l + b) h

, and total surface

2 (l b + bh + h l)

; a cube of edge

a

is the case

l = b = h = a

, with volume

a^{3}

and surface

6 a^{2}

How to use it

1The four walls exclude the floor and the ceiling; a question about painting or papering walls wants $2 (l + b) h$ , not the total surface.
2Read $V = (cross-section) \times (length)$ backwards to recover a bar's thickness from its volume and length.
3A volume spread to a uniform depth over a flat area obeys $V = area \times depth$ , which is the same formula with the area taken whole.

A room is

6

m long,

4

m broad and

3

m high. Find the area of its four walls.

Step-by-step

1
$2 (l + b) h = 2 (6 + 4) (3)$
Why: The four walls form a band of height $h$ around a perimeter of $2 (l + b)$ .
2
$= 60$ m $^{2}$

Answer

60

^{2}

Watch out

Keep the three measurements in one unit before multiplying, since a single slip changes the answer by a factor of

100

or more. The floor is

l b

, one long wall is

l h

and the pair of long walls is

2 l h

— all different from the four-wall total.

Also known as

volume of a cuboid, area of four walls, lateral surface of a cuboid, volume of a cube, 2(l+b)h