Solid | Picture | Dimensions | Equation | Volume | Surface Area |
---|---|---|---|---|---|
Cube | side length, a |
0 < x < a
0 < y < a 0 < z < a |
a^{3} | 6a^{2} | |
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 |
x^{2} + y^{2}
< a^{2}
0 < z < h |
πa^{2}h | 2πa(a+h) | |
Cone^{†} | radius, a
height, h |
x^{2} + y^{2}
< (az/h)^{2}
0 < z < h |
^{1}/_{3}πa^{2}h | πa√(a^{2}+h^{2}) + πa^{2} | |
Sphere | radius, a | x^{2} + y^{2} + z^{2} < a^{2} | ^{4}/_{3}πa^{3} | 4πa^{2} | |
Ellipsoid | principal axes a, b, and c |
(x/a)^{2} + (y/b)^{2} + (z/c)^{2} < 1 | ^{4}/_{3}πabc | - |
† These two solids are not in their most general form, but are of the "right-circular" variety