Volume of cylindrical hole = π × (1 cm)^2 × 8 cm = 8π cubic cm - Appfinity Technologies

Understanding the Context

Calculating Volume Step-by-Step

Given:

• Radius (r) = 1 cm
  
• Height (h) = 8 cm

The formula becomes:
Volume = π × (1 cm)² × 8 cm

Since the square of the radius (1 cm) is just 1 cm², the calculation simplifies to:
Volume = π × 1 × 8 = 8π cubic centimeters

Key Insights

Why This Formula Works

Cylinders are defined by their circular cross-section and the distance between two parallel bases (height). The area of the circular base is πr², and multiplying this by the height gives the total volume.

For the hole in question:

• Base area = π × (1 cm)² = π cm²
  
• Depth (height) = 8 cm
  
• Volume = base area × height = π × 1 × 8 = 8π cm³

Real-World Applications

Understanding this formula helps in:

Final Thoughts

• Material estimation: Calculating material removal when drilling holes.
  
• Fluid dynamics: Determining volume of cylindrical voids in pipes or tanks.
  
• Manufacturing: Precisely designing components with internal cavities.
  
• Education: Teaching fundamental geometry and physics principles.

Summary

To find the volume of a cylindrical hole, plug the radius and height into V = πr²h. For a hole with 1 cm radius and 8 cm depth:
V = π × 1² × 8 = 8π cm³

This simple yet powerful formula enables accurate volume calculations in countless practical scenarios. Mastering it supports better design, budgeting, and problem-solving in science and industry.

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