**Surface
Area of a Cuboid**

A cuboid is a three-dimensional (3D)
solid shape bounded by six rectangular faces. A cuboid and its net are shown
below. The area of the net of the cuboid is called the surface area of the
cuboid.

Thus, to calculate the surface area of a cuboid, we find the area of all six rectangular faces and add them.

Therefore,
the surface area of a cuboid is equal to the sum of the areas of its six
rectangular faces.

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

Surface area of the cuboid = Sum of areas of six rectangular faces

=
2 × *l *× *b *+ 2 × *l *× *h *+ 2 × *b *× *h *

=
2(*lb *+ *bh *+ *hl*) sq. units

Surface area of the cuboid =
2(*lb *+ *bh *+ *hl*)

**Surface
Area of a Cuboid Formula**

**Surface area of a cuboid = 2( lb
+ bh + hl)**

**Lateral Surface Area of a Cuboid
Formula**

Lateral surface
area is the sum of the areas of four faces except top and bottom faces of the
cuboid.

Lateral surface
area of the cuboid = 2 × *l *× *h *+ 2 × *b *× *h *

*
*= 2*h*(*l *+ *b*) sq. units

Thus, lateral surface area
of a cuboid = 2(*l *+ *b*) × *h *sq. units

**Area of Four Walls of a Room Formula**

We can observe that a room is in the
shape of a cuboid. So, the area of four walls of a room is equal to the lateral
surface area of the cuboid.

Thus, area of four walls of a room = Lateral
surface area of the room

= 2 × *l *× *h *+ 2 × *b *× *h
*

*
*=
2*h*(*l *+ *b*) sq. units

Area of four walls of a room
= 2*h*(*l *+ *b*) sq. units

**Surface Area of a Cuboid Example**

**Example
1: **Find the total
surface area and the lateral surface area of a cuboid measuring 12 cm by 10 cm
by 8 cm.

**Solution: **Given: *l *=
12 cm, *b *= 10 cm and *h *= 8 cm

Total
surface area of a cuboid = 2 (*lb *+ *bh *+ *lh*)

= 2 × (12 × 10 + 10 × 8 + 8 × 12)

=
2 (120 + 80 + 96)

= 2
(296) = 592 sq. cm

Lateral
surface area = 2 (*l *+ *b*) *h *

* *= 2 (12 + 10) × 8

= 352 sq. cm

**Example 2:** A rectangular
box of wood measures 20 cm by 15 cm by 10 cm. Find the total surface area of
the wooden box. Also, find the cost of making the wooden box at Rs 2 per sq.
cm.

**Solution: **Given: *l* = 20 cm, *b*
= 15 cm and *h* = 10 cm

Total
surface area of the wooden box = 2 × (*lb *+ *bh *+ *lh*)

=
2 × (20 × 15 + 15 × 10 + 10 × 20)

= 2 × (300 + 150 + 200) = 1300
sq. cm

Cost of making the wooden box = Rs 2 ×
1300 = Rs 2600

**Example 3: **Find
the cost of making a rectangular tank without a lid 4 m long, 3 m

wide and 2 m deep, at Rs 1000 per sq. m.

**Solution: **Length
of the tank = 4 m; breadth of the tank = 3 m and height of the tank =

2 m

Area of the four walls of the tank = 2*h*(*l
*+ *b*)

= 2 × 2(4
+ 3) = 28 sq. m

Area of the floor = *l *× *b *=
4 × 3 = 12 sq. m

Total surface area of the tank = 28 + 12
= 40 sq. m

Cost of making the tank = 40 × 1000 = Rs 40,000