Real-World Examples of Perfect Cubes and Cube Roots

📚 Quick Study Guide

• 🔢 A perfect cube is a number that can be obtained by cubing an integer (raising it to the power of 3). For example, $2^3 = 8$, so 8 is a perfect cube.
• ➗ A cube root is a value that, when multiplied by itself three times, gives you the original number. The cube root of 8 is 2, written as $\sqrt[3]{8} = 2$.
• 📐 Perfect cubes often appear in geometry when calculating the volume of cubes.
• 👷 Real-world examples include packing problems (e.g., how many small cubic boxes fit perfectly into a larger cubic container) and engineering calculations.
• 💡 The formula for the volume of a cube with side 's' is $V = s^3$.

🧪 Practice Quiz

1. What is the cube root of 27?
1. 2
2. 3
3. 4
4. 9
2. A cube has a side length of 5 cm. What is its volume?
1. 15 cm³
2. 25 cm³
3. 125 cm³
4. 625 cm³
3. Which of the following numbers is a perfect cube?
1. 10
2. 16
3. 64
4. 50
4. A cubic container has a volume of 1000 cubic inches. What is the length of one side?
1. 5 inches
2. 10 inches
3. 20 inches
4. 30 inches
5. What is the value of $\sqrt[3]{125}$?
1. 4
2. 5
3. 6
4. 7
6. If a cube has a volume of 216 $cm^3$, what is the length of one of its sides?
1. 4 cm
2. 5 cm
3. 6 cm
4. 7 cm
7. Which real-world application commonly uses calculations involving perfect cubes?
1. Baking recipes
2. Calculating gas mileage
3. Determining the area of a circle
4. Volume calculations for cubic containers