Bangun Ruang Sisi Lengkung [Part 3] - Bola

Introduction

This tutorial provides a comprehensive guide to understanding and calculating properties of a sphere (bola) as discussed in the video "Bangun Ruang Sisi Lengkung [Part 3] - Bola" by Benni Al Azhri. This content is especially relevant for ninth-grade students studying geometry during distance learning. We will cover the definition of a sphere, how to calculate its surface area, and how to find its volume.

Step 1: Understand the Definition of a Sphere

• A sphere is a perfectly round three-dimensional shape.
• It is defined as the set of all points in space that are equidistant from a central point, known as the center.
• The distance from the center to any point on the sphere is called the radius.

Key Terms

• Radius (r): The distance from the center of the sphere to its surface.
• Diameter (d): The distance across the sphere, passing through the center. It is twice the radius (d = 2r).

Step 2: Calculate the Surface Area of a Sphere

The formula to calculate the surface area (A) of a sphere is:

A = 4 × π × r²

Steps to Calculate Surface Area

1. Identify the radius of the sphere.
2. Square the radius (multiply the radius by itself).
3. Multiply the squared radius by π (approximately 3.14).
4. Multiply the result by 4 to find the surface area.

Example Calculation

If the radius (r) is 10.5 cm

• ( r² = 10.5² = 110.25 )
• ( A = 4 × π × 110.25 ≈ 4 × 3.14 × 110.25 ≈ 1382.3 ) cm².

Step 3: Calculate the Volume of a Sphere

The formula to calculate the volume (V) of a sphere is:

V = (4/3) × π × r³

Steps to Calculate Volume

1. Identify the radius of the sphere.
2. Cube the radius (multiply the radius by itself twice).
3. Multiply the cubed radius by π.
4. Multiply the result by 4 and then divide by 3 to find the volume.

Example Calculation

If the radius (r) is 18 cm

• ( r³ = 18³ = 5832 )
• ( V = (4/3) × π × 5832 ≈ (4/3) × 3.14 × 5832 ≈ 24454.4 ) cm³.

Conclusion

In this tutorial, we explored the definition of a sphere and how to calculate its surface area and volume. Remember the key formulas:

• Surface Area: ( A = 4 × π × r² )
• Volume: ( V = (4/3) × π × r³ )

To practice, try calculating the surface area and volume for different radius values. This will help reinforce your understanding of the properties of spheres. Keep studying and stay healthy!