Question

Derive the formula to find total surface area of a cuboid(Proper illustration and formula should be shown with an example


pls give a proper solution I have a project work on it:)​

Answer 1

Step-by-step explanation:

Sets & Set Theory

Statistics

Vectors

Home > Surface Area Of A Cuboid – Explanation & Examples

Surface Area of a cuboid – Explanation & Examples

Before we get started, let’s discuss what a cuboid is. A cuboid is one of the most common shapes in the environment around us. For example, a brick, a matchbox, a chalk box, etc., are all cuboids.

In geometry, a cuboid is a 3-dimensional figure with a length, width, and height. A cuboid has 6 rectangular faces. Ultimately, a cuboid has the shape of a rectangular prism or a box.

In a cuboid, the horizontal longer side is the length (l), and the shorter horizontal side is the width (w) or breadth (b). The height (h) of a cuboid is the vertical side.

The surface area of a cuboid is the sum of the area of the 6 rectangular faces that cover it.

Surface area of cuboid = 2lw + 2lh + 2wh

Note: The cuboid’s total surface area is not the same as the lateral surface area of a cuboid. The lateral surface of a cuboid is the sum of the area of the rectangular faces excluding the top and bottom face;

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

Surface area of a cuboid formula

From the above illustration, the formula for the total surface area of a cuboid can be represented as:

Total surface area of a cuboid (TSA) = 2 (lw + wh + lh)

The units for the surface area of a cuboid are square units.

Let’s practice some example problems below.

Example 1

The dimensions of a cuboid are given as follows:

Length = 5 cm

Width = 3 cm

Height = 4 cm.

Find the total surface area of the cuboid.

Solution

By the formula,

Total surface area of a cuboid = 2 (lw + wh + lh)

Substitute.

TSA = 2(5 x 3 + 3 x 4 + 5 x 4)

= 2(15 + 12 + 20)

= 2(47)

= 2 x 47 = 94 cm2

Therefore, the total surface area of the cuboid is 94 cm2