Assembling the Body
Now to put all the pieces together!
The total volume can be calculated by simply adding up the volumes of each of the parts that the body's
composed of,
but to calculate the total surface area requires a bit more work.
In order to calculate the surface area, we must first calculate the common area between shapes where they
overlap.
The common area needs to be subtracted twice,
since both shapes have overlapping area.
Volume
VTotal =
VMain Body + 2VLeg + 2VArm + VNeck
+ VHead
Adult:
V = 34812.8364 + 2×9882.2885 + 2×3232.8777 + 974.8240 + 4426.7901
V = 66444.7829
V ≈ 66445 cm3
Infant:
V = 278.5027 + 2×79.0609 + 2×25.8630 + 7.7988 + 35.4143
V = 531.5636
V ≈ 532 cm3
Common Area b/w Legs & Body
A = ALeg Cap
A = πrLeg2
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Adult:
A = π×6.04792
A = 114.9103 cm2
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Infant:
A = π×1.20962
A = 4.5966 cm2
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Common Area b/w Arms & Body
A = AArm Cap
A = πrArm2
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Adult:
A = π×3.97892
A = 49.7366 cm2
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Infant:
A = π×0.79582
A = 1.9896 cm2
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Common Area b/w Neck & Body
A = ANeck Cap
A = πrNeck2
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Adult:
A = π×5.57042
A = 97.4816 cm2
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Infant:
A = π×1.11412
A = 3.8994 cm2
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Common Area b/w Head & Neck
A = ANeck Cap
A = πrNeck2
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Adult:
A = π×5.57042
A = 97.4816 cm2
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Infant:
A = π×1.11412
A = 3.8994 cm2
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Total Surface Area
ATotal =
AMain Body + 2(ALeg - 2ACommon Leg/Body)
+ 2(AArms - 2ACommon Arm/Body) + ANeck - 2ACommon Neck/Body
+ AHead - 2ACommon Head/Neck
Adult:
A =
6330.9888 + 2(3497.8272 - 2×114.9103)
+ 2(1724.4840 - 2×49.7366) + 544.9648 - 2×97.4816
+ 1303.7973 - 2×97.4816
A = 17575.8593
A ≈ 17576 cm2
Infant:
A =
253.2396 + 2(139.9156 - 2×4.5966)
+ 2(68.9794 - 2×1.9896) + 21.7990 - 2×3.8994
+ 52.1519 - 2×3.8994
A = 703.0381
A ≈ 703 cm2
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