Rumus Luas dan Volume Bangun Ruang Sisi Lengkung // Tabung, Kerucut, dan Bola

Introduction

This tutorial covers the concepts of curved space figures, specifically focusing on the cylinder, cone, and sphere. We will explore their properties, formulas for surface area and volume, and how to apply these concepts in practical scenarios. Understanding these figures is essential for students in grade 9 as it builds a foundation for more advanced mathematical concepts.

Step 1: Understanding Curved Space Figures

Curved space figures consist of three main types:

• Cylinder
• Cone
• Sphere

Properties of Each Figure

• Cylinder

  • Has two circular bases and a curved surface.
  • Height is the distance between the two bases.

• Cone

  • Has a circular base and a pointed top (apex).
  • The slant height is the distance from the base to the apex along the surface.

• Sphere

  • A perfectly round three-dimensional shape where every point on the surface is equidistant from the center.

Step 2: Key Formulas for Surface Area and Volume

Each figure has unique formulas that are essential for calculations.

Cylinder

• Surface Area:

  • Formula: ( A = 2\pi r(h + r) )
    • Where ( r ) is the radius and ( h ) is the height.

• Volume:

  • Formula: ( V = \pi r^2 h )

Cone

• Surface Area:

  • Formula: ( A = \pi r (r + s) )
    • Where ( r ) is the radius and ( s ) is the slant height.

• Volume:

  • Formula: ( V = \frac{1}{3} \pi r^2 h )

Sphere

• Surface Area:

  • Formula: ( A = 4\pi r^2 )

• Volume:

  • Formula: ( V = \frac{4}{3} \pi r^3 )

Step 3: Visualizing the Figures

Creating nets (or jarring) for each figure can help in understanding their three-dimensional shapes.

Cylinder Net

• Comprises two circles (bases) and a rectangle (curved surface).

Cone Net

• Consists of one circle (base) and a sector of a larger circle that forms the curved surface.

Sphere Net

• Cannot be represented as a net but can be visualized as being formed by rotating a circle around an axis.

Step 4: Practical Applications

Understanding and calculating the properties of these shapes can be applied in real-world scenarios:

• Construction: Calculating materials needed for cylindrical pipes or conical roofs.
• Manufacturing: Designing spherical tanks or containers.
• Science: Analyzing the properties of various liquids held in different shapes.

Conclusion

In this tutorial, we covered the types of curved space figures, their properties, and the formulas needed to calculate surface areas and volumes. Mastering these concepts is crucial for solving mathematical problems related to these shapes. As a next step, practice calculating the surface area and volume using various examples, and consider how these shapes appear in real life to enhance your understanding.