The volumes of geometric shapes can be calculated from key measurements. This can be used to determine the size of a variety of lesions such as tumors or infarcts.
|
Shape |
Formula |
Variables |
|
cube |
a^3 |
a = length of side |
|
box |
a * b * c |
a, b, c = lengths of sides |
|
cylinder |
π * (R^2) * h |
R = radius of base h = height |
|
cone |
1/3 * π * (R^2) * h |
R = radius of base h = height |
|
truncated cone (frustrum) |
1/3 * π *h *((R1^2) + (R2^2) + (R1*R2)) |
R1 = radius of base R2 = radius at top h = distance between planes |
|
pyramid with square base |
1/3 * (a^2) * h |
a = length of base h = height |
|
truncated pyramid with square base (frustrum) |
1/3 * h * ((a^2) + (b^2) + (a * b)) |
a = side at base b = side at top h = distance between planes |
|
sphere |
4/3 * π * (R^3) |
R = radius |
|
zone and segment of sphere with 1 base |
1/6 * π * ((3* (r^2)) + (h^2)) |
r = radius at base h = distance to top |
|
zone and segment of sphere with 2 bases |
1/6 * π * h * ((3* (r1^2)) + (3* (r2^2)) + (h^2)) |
r1 = radius at base r2 = radius at top h = distance between planes |
|
ellipsoid |
4/3 * π * a * b * c |
a, b, c = lengths of semiaxes |
|
torus |
2 * π * R * (r^2) |
R = radius from center of space enclosed by inner ring to center of cross-section; r = radius of cross-section |
where:
• The length of a semiaxis for an ellipsoid is half of the measurement along the axis. If the entire axial measurement is used, then the volume = 1/6 * π * a * b * c
