Surface Area, Polyhedra & Coating Calculator
Compute total and lateral surface areas of 3D solids, analyze Platonic polyhedra and frustums, and size paint coating or sheet metal requirements
Total Surface Area (TSA)
87.965 m²
Exact: 28.000π m²
Lateral (Curved): 62.832 m² • Bases: 25.133 m²
Lateral / Curved Surface Area
62.832 m²
Excluding top & bottom bases
Base Surface Area
25.133 m²
2 circular bases (2 × πr²)
Surface-to-Volume Ratio (A / V)
1.400 m⁻¹
Enclosed Volume: 62.832 m³
Characteristic Slant / Diagonal
6.403 m
Internal diagonal √(4r² + h²)
Total Polyhedron / Frustum Surface Area
2,130.56 cm²
Lateral Slant Area: 1,313.68 cm² • End Bases: 816.81 cm²
Individual Face Area
328.42 cm²
Average lateral face segment
Slant Height / Inradius
18.974 cm
s = √(h² + (R₂ – R₁)²)
Enclosed Volume (V)
6,986.9 cm³
6.987 Liters capacity
Area-to-Volume Ratio (A / V)
0.305 cm⁻¹
Structural compactness metric
Paint & Coating Parameters
Sheet Metal Cladding (Skin Weight)
e.g., 1.2 mm ≈ 18 Gauge steel
Total Liquid Coating Required
19.35 Liters
5.11 US Liquid Gallons (2 Coats with 10% Waste Margin)
Can Purchase Recommendation
1 × 20L Pail (or 5 × 4L)
Commercial packaging sizes
Effective Painted Surface Area
193.5 m²
Area × 2 coats × 1.10
Sheet Metal Skin Total Mass
828.6 kg
1,826.8 lbs (1.2 mm thickness)
Unit Surface Weight Density
9.42 kg / m²
1.93 lb / sq ft