Andrew Simmons 28 July 2007
Surface Area : Volume Ratios and Dehydration
 
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Calculations for each Part of the Body

Below I've calculated the volume and total surface area for each part of the body. For the purposes of this investigation, I used measurements of myself for the dimensions of an adult and assumed that an infant is 1/5 of that size.


Main Body

Adult:

h = 62 cm
C = 84 cm

C = 2πr
r = C / 2π
r = 13.3690 cm

A = 2πr2 + 2πrh
A = 6330.9888 cm2

V = πr2h
V = 34812.8364 cm3
Infant:

h = 62 / 5 = 12.4 cm
r = 13.3690 / 5 = 2.6738 cm

A = 2πr2 + 2πrh
A = 253.2396 cm2

V = πr2h
V = 278.5027 cm3

Legs

Adult:

h = 86 cm
C = 38 cm

C = 2πr
r = C / 2π
r = 6.0479 cm

A = 2πr2 + 2πrh
A = 3497.8272 cm2

V = πr2h
V = 9882.2885 cm3
Infant:

h = 86 / 5 = 17.2 cm
r = 6.0479 / 5 = 1.2096 cm

A = 2πr2 + 2πrh
A = 139.9156 cm2

V = πr2h
V = 79.0609 cm3

Arms


Adult:

h = 65 cm
C = 25 cm

C = 2πr
r = C / 2π
r = 3.9789 cm

A = 2πr2 + 2πrh
A = 1724.4840 cm2

V = πr2h
V = 3232.8777 cm3
Infant:

h = 65 / 5 = 13 cm
r = 3.9789 / 5 = 0.7958 cm

A = 2πr2 + 2πrh
A = 68.9794 cm2

V = πr2h
V = 25.8630 cm3

Neck

Adult:

h = 10 cm
C = 35 cm

C = 2πr
r = C / 2π
r = 5.5704 cm

A = 2πr2 + 2πrh
A = 544.9648 cm2

V = πr2h
V = 974.8240 cm3
Infant:

h = 10 / 5 = 2 cm
r = 5.5704 / 5 = 1.1141 cm

A = 2πr2 + 2πrh
A = 21.7990 cm2

V = πr2h
V = 7.7988 cm3

Head

Adult:

C = 64 cm

C = 2πr
r = C / 2π
r = 10.1859 cm

A = 4πr2
A = 1303.7973 cm2

V = (4/3)πr3
V = 4426.7901 cm3
Infant:

r = 10.1859 / 5 = 2.0372 cm

A = 4πr2
A = 52.1519 cm2

V = (4/3)πr3
V = 35.4143 cm3
Previous: Modelling the Human Body Next: Assembling the Body
This is a secondary school project (use with caution). See resources for references and image credits.