Solid figures

Lateral area of a rectangular (right) prism
S_son = P h

Surface area of a rectangular (right) prism
S = S_son + 2 * S_pagr

Volume of a rectangular (right) prism
V = S_pagr * h

Diagonal of a rectangular parallelepiped
d^2 = a^2 + b^2 + c^2

Lateral area of a rectangular parallelepiped
S_son = 2(ac+bc)

Surface area of a rectangular parallelepiped
S_son = 2(ab + bc + ac)

Volume of a rectangular parallelepiped
V = S_pagr*h

Volume of a rectangular parallelepiped
V = a b c

Lateral area of a cube
S_son = 4 a^2

Surface area of a cube
S = 6 a^2

Volume of a cube
V = a^3

Lateral area of a regular pyramid
S_son = 1/2 * P * h_s

Lateral area of a regular pyramid
S_son = S_pagr / cos(φ)

Volume of a regular pyramid
V = 1/3 * S_pagr * h

Lateral area of a frustum of a regular pyramid
S_son = 1/2 (P1 + P2) * h_s

Lateral area of a frustum of a regular pyramid
S_son = (S1 - S2) / cos(φ)

Surface area of a frustum of a pyramid
S = S_son + S1 + S2

Volume of frustum of a pyramid
V = 1/3 h (S1+S2+saknis(S1*S2))

Lateral area of a cylinder
S_son = 2 π r h

Area of a base of a cylinder
S_pagr = π r^2

Surface area of a cylinder
S = 2 π r ( r + h)

Volume of a cylinder
V = π r^2 h

Lateral area of a cone
S_son = π r l

Surface area of a cone
S = π r (r + l)

Lateral area of a cone (net)
S = π l^2 α / 360

Volume of a cone
V = 1/3 π r^2 h

Lateral area of a frustum of a cone
S_son = π (R + r) l

Surface area of a frustum of a cone
S = π (R + r) l + π*R^2 + π*r^2

Volume of a frustum of a cone
V = 1/3 π h (R^2 + r^2 + Rr)

Surface area of a sphere (ball)
S = 4 π * R^2

Volume of a sphere (ball)
V = 4/3 π * R^3

Surface area of a spherical cap (segment)
S = 2 π R h

Volume of a spherical cap (segment)
V = π h^2 ( R - h / 3)

Volume of a spherical cap (segment) using radius of base
V = 1/6 π h ( h^2 + 3 r^2)

Surface area of a spherical segment
S = 2π *R * h

Volume of a spherical segment
V = 1/6 π h^3  + 1/2 π( r1^2 + r2^2) h

Surface area of a spherical sector (cone)
S = π* R (2h + r)

Volume of a spherical sector (cone)
V = 2/3 π * R^2 h