Solved Examples on Surface Area of a Cuboid

Example 1: Determine the lateral surface area of a cuboid if its length, breadth, and height are 15 in, 8 in, and 12 in, respectively.

Solution:

Given data,

The length of a cuboid (l) = 15 in

The breadth of a cuboid (b) = 8 in

The height of a cuboid (h) = 12 in

We have,

Lateral surface area of a cuboid = 2h(l + b)

= 2 × 12 (15 + 8)

= 24 × 23 = 552 square inches.

Hence, the lateral surface area of the given cuboid is 552 square inches.

Example 2: What is the total surface area of a cuboid shown in the figure below:

Solution:

Given data,

The length of a cuboid (l) = 18 cm

The breadth of a cuboid (b) = 13 cm

The height of a cuboid (h) = 15 cm

We have,

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

= 2 [(18 × 13) + (13 × 15) + (18 × 15)]

= 2 [234 + 195 + 270]

= 2 [699] = 1398 cm²

Hence, the total surface area of the given cuboid is 1398 cm².

Example 3: Calculate the height of the cuboid whose lateral surface area is 360 square units and whose length and breadth are 12 units and 8 units, respectively.

Solution:

Given data,

The length of a cuboid (l) = 12 units

The breadth of a cuboid (b) = 8 units

The lateral surface area = 360 square units

We have,

Lateral surface area of a cuboid = 2h(l + b)

⇒ 2h (12 + 8) = 360

⇒ h × (20) = 360/2 = 180

⇒ 20h = 180⇒ h = 180/20

⇒ h = 9 units

Hence, the height of the given cuboid is 9 units.

Example 4: Determine the length and the total surface area of a cuboid whose lateral surface area is 960 sq. in and whose breadth and height are 12 in and 16 in, respectively.

Solution:

Given data,

The breadth of a cuboid (b) = 12 in

The height of a cuboid (h) = 16 in

The lateral surface area = 960 square inches

We know that,

Lateral surface area of a cuboid = 2h(l + b)

⇒ 2 × 16 (l + 12) = 960

⇒ 32 (l + 12) = 960

⇒ (l + 12) = 960/32 = 30

⇒ l = 30 – 12 = 18 in

We have,

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

= 2 [(18 × 12) + (12 × 16) + (18 × 16)]

= 2 [ 216 + 192 + 288]

= 2 × [696] = 1398 square inches

Hence, the length and the total surface area of the cuboid are 18 in and 1398 sq. in, respectively.

Example 5: Calculate the total surface area of a cuboid if its length, breadth, and height are 10 in, 5 in, and 8 in, respectively.

Solution:

Given data,

The length of a cuboid (l) = 10 in

The breadth of a cuboid (b) = 5 in

The height of a cuboid (h) = 8 in

We have,

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

= 2 [(10 × 5) + (5 × 8) + (10 × 8)]

= 2 × [50 + 40 + 80]

= 2 × (170) = 340 sq. in

Hence, the total surface area of the given cuboid is 340 sq. in.

Example 6: Determine the lateral and total surface areas of a cuboid whose length, breadth, and height are 21 cm, 16 cm, and 18 cm, respectively.

Solution:

Given data,

The length of a cuboid (l) = 21 cm

The breadth of a cuboid (b) = 16 cm

The height of a cuboid (h) = 18 cm

We have,

Lateral surface area of a cuboid = 2h(l + b)

= 2 × 18 (21 + 16)

= 36 × 37 = 1332 sq. cm

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

= 2 [(21 × 16) + (16 × 18) + (21 × 18)]

= 2 [336 + 288+ 378] = 2 × 1002

= 2004 sq. cm

Therefore, the lateral surface area and the total surface area of a cuboid are 1332 sq. cm and 2004 sq. cm, respectively.

The surface area of a cuboid is the total space occupied by all its surfaces/sides. In geometry, a three-dimensional shape having six rectangular faces is called a cuboid. A cuboid is also known as a regular hexahedron and has six rectangular faces, eight vertices, and twelve edges with congruent, opposite faces. It is a three-dimensional form of a rectangle with four lateral faces and two faces at the top and bottom. Some examples of cuboids that we regularly see are bricks, geometric boxes, shoe boxes, packaging boxes, etc. Let’s learn in detail about the surface area of a cuboid, along with examples.