Volume of a Cylinder

Volume Formula

• Volume of a cylinder is calculated as:

  • Formula: Volume = Area of Base × Height

  • The base of a cylinder is a circle.

Area of Circle

• Area of a circle formula:

  • Formula: Area = π × radius²

Volume Formula for Cylinder

• Combining the area and height of the cylinder:

  • Formula: Volume = π × radius² × height

Given Measurements

• Radius of the cylinder: 7 m

• Height of the cylinder: 10 m

Step-by-step Calculation

1. Plug in radius and height into the volume formula:

   • Volume = π × (7 m)² × 10 m

2. Calculate the area of the base:

   • (7 m)² = 7 m × 7 m = 49 m²

3. Substitute the area back into the volume formula:

   • Volume = π × 49 m² × 10 m

4. Simplify:

   • Volume = 490π m³

   • One representation of volume: 490π cubic meters

Approximation of π

• Use π ≈ 3.14 to calculate volume numerically:

  • Volume = 490 × 3.14 m³

Final Calculation

• Multiply to find approximate volume:

  • Volume ≈ 1,538.6 m³

Conclusion

• Two ways to express the volume of the cylinder:

  • Exact: 490π cubic meters

  • Approximate: 1,538.6 cubic meters.