Sphere (Ball)
Formula: A = 4πr²
Example: If r = 5, A = 4 × π × 25 = 314.16
Cone
Formula: A = πr(l + r), where l = √(r² + h²)
Example: r = 3, h = 4 → l = 5 → A = π × 3 × (3+5) = 75.4
Cube
Formula: A = 6a²
Example: a = 2 → A = 6 × 4 = 24
Cylinder (Tank)
Formula: A = 2πr(h + r)
r = 3, h = 5 → A = 2 × π × 3 × (5+3) = 150.8
Rectangular Tank (Cuboid)
Formula: A = 2(lw + lh + wh)
l=2, w=3, h=4 → A=2(6+8+12)=52
Capsule
Formula: A = 2πr(2r + h)
r = 2, h = 5 → A = 2π × 2 × (4 + 5) = 113.1
Spherical Cap
Formula: A = 2πrh
r = 5, h = 2 → A = 2π × 5 × 2 = 62.8
Ellipsoid
Formula: A ≈ 4π × ((a^p × b^p + a^p × c^p + b^p × c^p)/3)^(1/p), p ≈ 1.6075
a=3, b=4, c=5 → Approx A ≈ 212.6
Square Pyramid
Formula: A = a² + 2a × √(h² + (a²/4))
a=4, h=6 → A = 16 + 2×4×√(36+4)=73.29