Volume and Surface Area

Solid Picture Dimensions Equation Volume Surface Area
Cube side length, a 0 < x < a
0 < y < a
0 < z < a
a3 6a2
Cuboid length, a
width, b
height, c
0 < x < a
0 < y < b
0 < z < c
abc 2(ab+bc+ca)
Cylinder radius, a
height, h
x2 + y2 < a2
0 < z < h
πa2h a(a+h)
Cone radius, a
height, h
x2 + y2 < (az/h)2
0 < z < h
1/3πa2h πa√(a2+h2) + πa2
Sphere radius, a x2 + y2 + z2 < a2 4/3πa3 a2
Ellipsoid principal axes
a, b, and c
(x/a)2 + (y/b)2 + (z/c)2 < 1 4/3πabc -

† These two solids are not in their most general form, but are of the "right-circular" variety