How would you determine the surface area of a cow?

Question

You can't kill or harm the cow.

Answer 1

Do you need the actual surface area of a real cow? Or a good estimate?

For a good estimate, take three principal dimensions and calculate the surface area of a comparable ellipsoid. This will be close.

Now, the actual surface area of a cow is quite complicated. On a small scale, each hair has a surface area contribution, and that could be significant. When the cow opens its mouth, the surface area is greatly increased due to the lungs. All of this would be hard to calculate, but you could try:

Take a large room with a known volume of dry air. Get the cow wet, weigh it, then stick it in the room. Since we know the temperature of the cow, we can calculate the expected evaporation rate. Measure the humidity increase in the room and find what surface area of damp cow would lead to the increase. That would get you close to the real surface area.

Hope that helps.

Answer 2

Steps for determining the surface area of a cow.
1) Dip the cow in paint (I think fuschia or lime green would look good)
2) Measure the volume of remaining paint to calculate the how much paint was used
3) Let the paint dry and then peel off several portions. Measure the thickness of the paint and get an average.
4) Divide the volume of paint by the average thickness to get the surface area of the cow!

(Note: for steps 3 and 4, you might find a conversion chart on the paint can that says x gallons covers y sq. ft. of surface area. If so, that will simplify these two steps. Also, add breathing tubes and protection to the various orifices of the cow. A water-based paint will be easier to clean up later, so I would recommend that over acrylic and oil-based paints. And check fabric swatches in case you want to make some throw pillows to match your painted cow...)

Answer 3

1. Hi-Tech method:
Do a 3D optical scan of the cow and let the computer calculate the surface area.

2. Lo-Tech method:
Make a thigh fitting full body dress for the cow from X amount of cloth area. The surface area of the cow can be calculated from the remainder of the material, R.

Surface Area = X - R

Answer 4

Karman V is right on the money:

"For a good estimate, take three principal dimensions and calculate the surface area of a comparable ellipsoid. This will be close."

If it were a chicken, you would start by saying:

assuming a spherical chicken.....

Now for the cow you could divide it into several 3d objects such as a sphere for the head and an ellipsoid for the body, and 4 tiny cylinders for the legs, and then add all the surface areas of these known objects.

Answer 5

The surface area of a cow can't be determined exactly so you need a method to approximate it. I refer you to "Consider a Spherical Cow" I forget the author but I think there is a link to it on mathematicsteacher.org

Answer 6

use a digital camera to capture several photos of the cow, to make a 3D renderring of the cow. Make sure you have a reference for length in each picture to take, so the whole cow is to scale, and then let the computer figure out the surface area of the cow

Answer 7

First put some breathing apparatus on the cow, so we don't hurt them.
Next slowly place them in water and measure the displacement.
this will then enable you to work out the surface area.

alternatively your local vet may have tables that correlate weight to surface area, try that

Answer 8

you can draw little squares 1 cm by 1 cm on it. Then you count how many squares you have. Then you know the cow's surface in square centimetres. You could do the same by drawing squares 1 inch by 1 inch...then you got the surface in square inches... simple, easy and it won't harm the cow...
Success ;-)

Answer 9

Simple ask the cow!

Answer 10

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