Surface Area of a Cuboid

The amount of space surrounding a three-dimensional area is known as surface area. Here are the surface area and volume measurements for class 9 notes. This article discusses and fully explains the surface area formulas for cuboid. The surface area of a cuboid can be broadly divided into two categories: lateral surface area (LSA), and total surface area (TSA).

For any of the three-dimensional geometrical shapes, the surface areas and other geometrical entitites can be easily calculated. Keep reading to know more.

Surface Area of a Cuboid: Know The Formulas

Have a look at this section of the page to know the definition and formulas with regard to the Surface Area of a Cuboid:

Total Surface Area of a Cuboid

A three-dimensional shape is a cuboid. Six rectangular faces that are arranged at right angles make up the cuboid. The sum of the surfaces of a cuboid’s six rectangular faces determines its total surface area.

Consider a cuboid whose length is “l” cm, breadth is b cm and height h cm.
Area of face ABCD = Area of Face EFGH = (l × b) cm2
Area of face AEHD = Area of face BFGC = (b × h) cm2
Area of face ABFE = Area of face DHGC = (l × h) cm2
Total surface area (TSA) of Cuboid = Sum of the areas of all its six faces
= 2(l × b) + 2(b × h) + 2(l × h)= 2(lb + bh +lh)

Lateral Surface Area of a Cuboid

Lateral surface area (LSA) is defined as the area of all the sides excluding the top and bottom faces.
Thus, from the figure given above, the lateral surface area of the cuboid = Area of face AEHD + Area of face BFGC + Area of face ABFE + Area of face DHGC = 2(b × h) + 2(l × h)
LSA (cuboid) = 2h(l + b)

Applications of Cuboid in Daily Life

Cuboid shapes are frequently utilised for things like boxes, cabinets, rooms, buildings, containers, cabinets, books, a solid computer chassis, printing equipment, touchscreen phones, washing machines, and dryers, among other things. One of the solids that can tessellate three-dimensional space is the cuboid. The shape may hold numerous smaller cuboids, such as sugar cubes in a box, boxes in a cupboard, cupboards in a room, and rooms in a building, making it fairly adaptable.

For instance, a cuboid with sides 44, 117, and 240 is an Euler brick because it has integer edges and face diagonals. An Euler brick with a space diagonal that is also an integer is a perfect cuboid. Whether a perfect cuboid genuinely exists is unknown at this time.

Numericals on Surface Area of Cuboid

Following are some of the problem sums on the surface area of a cuboid that students may solve:

• Find the total surface area and the lateral surface area of a cuboid whose length = 6 inches, width = 4 inches, and height = 3 inches.
• The dimensions of a cuboid are given as: Length = 5 cm, Width = 8 cm. Height = 4 cm. Find the total surface area of the cuboid.
• The surface area of a cuboid is 126 ft². If the cuboid’s length and height are 6 feet and 3 feet, find the width of the cuboid.
• Given the dimensions of a cuboid as: Length = 10 m, Width = 5 width, Height = 9 m. By how much is the total surface area of the cuboid more than the lateral surface area?
• The length and width of a cardboard are 20 m by 10 m, respectively. How many cuboids can be made from the cardboard if each cuboid must be 4 m long, 3 m wide, and 1 m high.
• Compare the total surface area of a cube of length 8 cm and a cuboid of length 8 cm, width, 3 cm, and height, 4 cm.
• The surface area of a cuboid is 664 m². If the cuboid’s length and height are 8 meters and 10 meters, what is the width of the cuboid?

Hope this comprehensive article on “Surface Area of Cuboid” helped you for your Class 9 school board exam preparation.