0 < y < a
0 < z < a
width, b
height, c
0 < y < b
0 < z < c
height, h
0 < z < h
height, h
0 < z < h
a, b, and c
| 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 | 2πa(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 | 4πa2 |
| 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