Understanding the Dimensions of a 1 Litre Juice Carton

Understanding the Dimensions of a 1 Litre Juice Carton

Have you ever wondered about the dimensions of your everyday household items, such as a 1 litre juice carton? These seemingly simple objects can often present interesting geometric and mathematical challenges. In this article, we will explore the dimensions of a cuboid-shaped juice carton that has a square base and delve into the mathematical principles behind the volume calculation.

Introduction to Cuboid Dimensions

A cuboid is a three-dimensional shape with six faces, all of which are rectangles. It has three dimensions: length, width, and height. In the case of a 1 litre juice carton, the base is a square, meaning the length and width are the same.

Given Information and Objectives

Let's begin by understanding the given information about the juice carton. A 1 litre carton of juice is in the shape of a cuboid with a square base of size 8 cm by 8 cm. The objective is to determine the depth (height) of the juice in the carton.

Step-by-Step Calculation

Given:

The volume of the juice carton is 1 litre (1000 cc). The base of the carton is a square with a side length of 8 cm.

We need to find the height (h) of the carton. The formula for the volume of a cuboid is:

Volume length × width × height

Since the base is a square, the length and width are both 8 cm. Therefore, the formula for the volume of the carton can be written as:

Volume 8 cm × 8 cm × height (h)

We know that 1 litre is equivalent to 1000 cc, so we can set up the equation:

1000 cc 8 cm × 8 cm × height (h)

Simplifying this equation, we get:

1000 64 × height (h)

To solve for height (h), we need to divide both sides of the equation by 64:

height (h) 1000 / 64

Calculation:

height (h) 15.625 cm

Conclusion

The depth (height) of the juice in the 1 litre carton is 15.625 cm. This calculation highlights the importance of understanding basic geometric principles when dealing with everyday objects. Knowing the dimensions of different shapes helps in various practical applications, from packaging to storage.

Understanding such concepts is crucial for anyone working in fields such as engineering, packaging design, and even everyday problem-solving. By mastering these calculations, you can better understand the dimensions of the products you use and make more informed decisions about space and storage.