Frustum Surface Area Calculator & Formula Analysis

Base Radius (r, cm):

Top Radius (r', cm):

Slant Height (l, cm):

Precision Note: Results rounded to 4 decimal places for educational reference.

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Historical Origins & Formula Explanation

The frustum surface area formula has its roots in ancient geometric studies, with early developments in Greek and Islamic mathematics. The modern formula combines the areas of the two circular bases and the lateral (curved) surface area:

Where:
- \( r \) is the base radius
- \( r' \) is the top radius
- \( l \) is the slant height

This formula is widely used in engineering, architecture, and manufacturing for calculating material requirements in conical frustum structures.