3D GEOMETRY FORMULAE

CUBE

d = side

VOLUME : V = d^2

SURFACE AREA : S = 6(d^2)

RECTANGULAR SOLID

l = length, w = width, h = height

VOLUME: V = lwh

SURFACE AREA : S = 2lw + 2lh + 2wh

SPHERE

r = radius

VOLUME : V = 4/3*pi*r^3

SURFACE AREA : S = 4*pi*r^2

RIGHT CIRCULAR CYLINDER

r = radius, h = height

VOLUME : V = pi*r^2*h

SURFACE AREA : S = 2*pi*r*h + 2 *pi*r^2

TORUS

r = tube radius, R = torus radius

VOLUME : V = 2*pi^2*r^2*R

SURFACE AREA : S = 4*pi^2*r*R

PYRAMID

A = area of base , h = height

VOLUME : V = 1/3*A*h

RIGHT CIRCULAR CONE

r = radius, h = height

VOLUME : V = 1/3*pi*r^2*h

SURFACE AREA : S = pi*r*[sqrt(r^2 + h^2)] + pi*r^2

FRUSTUM OF A CONE

r = radius, R = base radius, h = height, s = slant height

VOLUME : V = pi/3(r^2 + rR + R^2)h

SURFACE AREA : S = pi*s(R+r) + pi*r^2 + pi*R^2

SQUARE PYRAMID

s = side, h = height

VOLUME : V = 1/3*s^2*h

SURFACE AREA : S = s(s + [sqrt(s^2 + 4 *h^2)])

REGULAR TETRAHEDRON

s = side

VOLUME : V = 1/12*sqrt(2s^2)

SURFACE AREA : S = sqrt(3s^2)

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