Splung.com Physics Forum

[Lost_student]

A physician uses ultrasound to measure the diameter of a fetus’s head as 4.16cm.

(1) Treating the head as a sphere, what’s its volume?

(2) Assuming the head density is 1020kg m-3 what’s its weight?

(3) Discuss your use of significant figures.

If you could help me work out this one, I have attempted this so many times and keep getting different answers. This question was taken from the biological physics book.

Thank you in advance

[hepcj]

It is quite simple. The volume is just the volume of a sphere of radius r= 4.16/2 cm. The volume of a sphere is V = 4/3 pi r^3.
Once you have the volume you can calculate the weight. The density of an object is mass/volume.
Rearrange for mass. You have calculated the volume in part 1 and the density is given.

The most interesting part of the question is about how many significant figures you should quote the answers. How many figures do you think it is reasonable to give the answer? You have used at least two approximations:

i) the assumption of a spherical head. Real heads are not completely symmetrical. In physics we are always approximating complex shapes by spheres. We even have a joke about it. A farmer asks a physicist to improve the milk yield of his cows. The physicist works on the problem and a month later the farmer gets the report. When he reads the report it starts, "Consider a spherical cow.."

ii) you have assumed a uniform density to calculate the weight. Obviously a real head is made of different tissues, a skull which is made of bone, skin which has a different density and brain which has a density that is close to water. The density quoted is some average of the different materials.