Math

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Frustum Cone Area Calculator.

Calculate lateral and total surface area of a right circular frustum.

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Results update as you type.

Lateral area: 100.530965 units²

Lateral area

0.000000units²
Base area: 106.81415 units²

Base area

0.000000units²
Total area: 207.345115 units²

Total area

0.000000units²

Results update automatically as you type.

Use Cases

Construction and Design

Determine the amount of material needed for a frustum-shaped object, such as a bucket, lampshade, or architectural element.

Example: Calculate the surface area of a bucket with radii 10 and 8 units and slant height 12 units.

Manufacturing and Fabrication

Estimate the surface area for painting, coating, or plating a frustum-shaped component in industrial processes.

Example: Find the total surface area of a metal funnel with radii 5 and 2 units and slant height 7 units.

Frequently Asked Questions

What is a frustum cone?
A frustum cone is the portion of a right circular cone left after cutting off the top by a plane parallel to the base. It has two circular bases of different radii.
How is the lateral surface area calculated?
The lateral surface area is calculated using the formula π * (larger radius + smaller radius) * slant height. This gives the area of the curved surface between the two bases.
What is the total surface area?
The total surface area is the sum of the lateral surface area and the areas of both circular bases. It is calculated as lateral area + π * (larger radius² + smaller radius²).

Tips & Common Mistakes

Tips

  • Ensure all input values are in the same unit (e.g., all in meters or all in feet) to get the area in square units.
  • The slant height is the distance along the sloped side, not the vertical height. Use the correct measurement for accurate results.
  • Double-check that the larger radius is greater than the smaller radius; if not, swap them to avoid negative results.
  • For a quick estimate, you can use approximate values of π (like 3.14) if you don't need high precision.

Common Mistakes to Avoid

  • Using the vertical height instead of the slant height. The slant height is the hypotenuse of the right triangle formed by the height and the difference in radii.
  • Forgetting to add the areas of both circular bases when calculating total surface area, resulting in only the lateral area.
  • Mixing units (e.g., using meters for radii and centimeters for slant height) without converting, leading to incorrect area units.

Last updated: August 13, 2026