Calculating the Surface Area of a Cuboid

Oct 13, 2025 by pinkandtrash.com 68 views

Calculating the Surface Area of a Cuboid: A Real-World Application of Math

In this article, we will explore the concept of surface area and how it applies to real-world problems. Michiko has a metal container in the shape of a cuboid, with a length of 2.5 m, a width of 2 m, and a height of 3 m. She plans to paint all the outside faces of the container with two coats of metal paint. To determine the amount of paint needed, we need to calculate the surface area of the container.

Surface area is the total area of the surface of a three-dimensional object. It is an important concept in mathematics and has numerous applications in real-world problems. In the case of a cuboid, the surface area can be calculated by finding the area of each face and adding them together.

Calculating the Surface Area of a Cuboid

The surface area of a cuboid can be calculated using the following formula:

SA = 2lw + 2lh + 2wh

Where:

SA is the surface area
l is the length
w is the width
h is the height

In this case, the length (l) is 2.5 m, the width (w) is 2 m, and the height (h) is 3 m. Plugging these values into the formula, we get:

SA = 2(2.5)(2) + 2(2.5)(3) + 2(2)(3) SA = 10 + 15 + 12 SA = 37

So, the surface area of the cuboid is 37 square meters.

Calculating the Total Area to be Painted

Since Michiko plans to paint two coats of metal paint, we need to calculate the total area to be painted. The surface area of the cuboid is 37 square meters, and since she is applying two coats, we need to multiply this by 2:

Total Area = 37 x 2 Total Area = 74

Determining the Amount of Paint Needed

The size of the paint tin is 250ml. To determine the amount of paint needed, we need to divide the total area to be painted by the area covered by one tin of paint. However, we do not know the area covered by one tin of paint. We will assume that the area covered by one tin of paint is equal to the surface area of the cuboid.

Area covered by one tin of paint = 37 square meters

To determine the number of tins of paint needed, we can divide the total area to be painted by the area covered by one tin of paint:

Number of tins of paint needed = Total Area / Area covered by one tin of paint Number of tins of paint needed = 74 / 37 Number of tins of paint needed = 2

So, Michiko will need 2 tins of paint to cover the entire surface area of the container.

In this article, we explored the concept of surface area and how it applies to real-world problems. We calculated the surface area of a cuboid and determined the amount of paint needed to cover the entire surface area. This problem demonstrates the importance of math in real-world applications and how it can be used to solve everyday problems.

Math is an essential part of our daily lives, and it has numerous applications in real-world problems. Some examples of real-world applications of math include:

Architecture: Math is used to design buildings and structures, taking into account factors such as size, shape, and weight.
Engineering: Math is used to design and develop new technologies, such as bridges, roads, and buildings.
Science: Math is used to describe the laws of physics and to model complex systems.
Finance: Math is used to calculate interest rates, investments, and risk management.

Math is a powerful tool that can be used to solve a wide range of problems. In this article, we explored the concept of surface area and how it applies to real-world problems. We calculated the surface area of a cuboid and determined the amount of paint needed to cover the entire surface area. This problem demonstrates the importance of math in real-world applications and how it can be used to solve everyday problems.