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When calculating the volume of a cube, you are essentially determining how much space is contained within it. A cube is a special type of geometric figure, where all three dimensions—length, width, and height—are equal. The formula for finding the volume of any cube is fairly straightforward:
\[ V = a^3 \]
where \( a \) represents the length of one side of the cube.In our exercise, the side of the cube is given as 15 cm. Therefore, the volume calculation involves cubing this side length:

• Start by cubing the side length: \( 15^3 \)
• Calculate the result: \( 15 \times 15 \times 15 = 3375 \text{ cm}^3 \)

This calculation provides the nominal volume of the cube, meaning that's the estimated volume without considering any uncertainty in the measurement.

In real-world scenarios, measurements are rarely exact. This is where the concept of uncertainty in measurement comes into play. Uncertainty tells us about the potential error in a measurement, helping us understand how accurate or reliable a measurement is.
In the given exercise, the length of the cube's side is provided as \( 15 \pm 0.2 \text{ cm} \). This means that the actual side length could vary between 14.8 cm and 15.2 cm.To factor this uncertainty into our volume calculation, consider both extreme values the side could take:

• Minimum possible side length: 14.8 cm
• Maximum possible side length: 15.2 cm

Calculating the volume for these lengths gives us a range:

• The smallest possible volume is \( 14.8^3 = 3241.792 \text{ cm}^3 \)
• The largest possible volume is \( 15.2^3 = 3511.168 \text{ cm}^3 \)

This range, from 3241.792 cm³ to 3511.168 cm³, effectively acknowledges the uncertainty involved in the side length measurement.

Geometric figures are shapes or forms that are defined and classified based on the dimensions, such as length, width, height, and angles. A cube is one of the simplest forms of a three-dimensional geometric figure, characterized by its equal sides and angles. Understanding the properties of geometric figures, like a cube, is essential in performing calculations related to volume, surface area, and more. A cube, in particular, stands out for its symmetry and simplicity, making calculations using cubes straightforward as each side is equal. Other common three-dimensional geometric figures include:

• Sphere
• Cylinder
• Cone

Each of these figures has its own specific formula for calculating volumes and areas, and learning about them expands our ability to solve various geometric problems efficiently. However, when dealing with cubes, the main aspect to remember is the equal side lengths, simplifying the volume calculation process significantly.