Surface Area of a Cuboid Formula

# Surface Area of a Cuboid Formula

## 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

= 2h(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

= 2h(l + b) sq. units

Area of four walls of a room = 2h(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 = 2h(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