What is Packing Cubes into a Cuboid?

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Grade Level:

Class 2

All STEM domains, Finance, Economics, Data Science, AI, Physics, Chemistry

Definition

What is it?

Packing cubes into a cuboid means figuring out how many small cube-shaped boxes can fit perfectly inside a larger rectangular box without any empty space. It's about using the volume of both shapes to find out how many times the smaller volume fits into the larger one.

Simple Example

Quick Example

Imagine you have a big carton box that your new TV came in. You also have many small, identical cube-shaped gift boxes. Packing cubes into a cuboid is like finding out how many of these small gift boxes can fit inside the big TV carton.

Worked Example

Step-by-Step

Let's say you have a big cuboid box (like a school bag) that is 30 cm long, 20 cm wide, and 10 cm high. You want to pack small cube-shaped tiffin boxes, each with a side of 10 cm.

Step 1: Find the volume of the big cuboid box. Volume = Length x Width x Height = 30 cm x 20 cm x 10 cm = 6000 cubic cm.
---Step 2: Find the volume of one small cube-shaped tiffin box. Volume = Side x Side x Side = 10 cm x 10 cm x 10 cm = 1000 cubic cm.
---Step 3: Divide the volume of the big box by the volume of one small tiffin box to find how many tiffin boxes fit. Number of tiffin boxes = Volume of big box / Volume of small box = 6000 cubic cm / 1000 cubic cm = 6.
---Answer: You can pack 6 small cube-shaped tiffin boxes into the big cuboid box.

Why It Matters

This concept is super useful in real life, from logistics to architecture. Companies like Flipkart and Amazon use it to efficiently load delivery trucks, saving fuel and time. Engineers use it to design storage spaces and even plan how to stack goods in a warehouse.

Common Mistakes

MISTAKE: Students sometimes only divide the length, width, and height separately and then multiply those results, without considering if the small cube's side fits evenly into each dimension. | CORRECTION: Always calculate the total volume of the cuboid and the total volume of the cube first, then divide the larger volume by the smaller volume.

MISTAKE: Forgetting that all sides of a cube are equal when calculating its volume. | CORRECTION: Remember that a cube has length = width = height, so its volume is side x side x side.

MISTAKE: Mixing up units, for example, using cm for the cuboid and meters for the cube. | CORRECTION: Always make sure all measurements are in the same units (e.g., all in cm or all in meters) before doing any calculations.

Practice Questions

Try It Yourself

QUESTION: A rectangular carton is 40 cm long, 20 cm wide, and 10 cm high. How many cube-shaped blocks with a side of 10 cm can fit inside? | ANSWER: 8 blocks

QUESTION: A storage room is 5 meters long, 4 meters wide, and 3 meters high. How many cube-shaped boxes, each with a side of 1 meter, can be stored in it? | ANSWER: 60 boxes

QUESTION: A large suitcase measures 60 cm x 40 cm x 20 cm. You want to pack small cube-shaped gift boxes, each with a side of 5 cm. How many such gift boxes can fit inside the suitcase? | ANSWER: 384 boxes

MCQ

Quick Quiz

What is the volume of a cube with a side of 5 cm?

25 cubic cm

125 cubic cm

15 cubic cm

100 cubic cm

The Correct Answer Is:

The volume of a cube is calculated by multiplying its side length by itself three times (side x side x side). So, 5 cm x 5 cm x 5 cm = 125 cubic cm.

Real World Connection

In the Real World

Think about how delivery services like Zepto or Dunzo pack items into their delivery bags or vehicles. They use this concept to make sure they can carry as many orders as possible in one trip, especially for items like grocery boxes. Also, in construction, this helps calculate how many bricks (cubes) are needed for a wall (cuboid section).

Key Vocabulary

Key Terms

CUBE: A 3D shape with 6 equal square faces, all sides are the same length. | CUBOID: A 3D shape with 6 rectangular faces, like a box. | VOLUME: The amount of space a 3D object occupies. | PACKING: Arranging objects efficiently into a container.

What's Next

What to Learn Next

Next, you can learn about 'Packing Cuboids into a Cuboid'. This will teach you how to fit smaller rectangular boxes into a larger rectangular box, which is even more common in real-world scenarios like packing a moving truck! Keep practicing!