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# help! dimension problem

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The Dictyostelium discoideum is an amoeba, a single-celled organism. Under ordinary circumstances, when viewed under a microscope, the amoebas will look like separate individual cells.

Dictyostelium discoideum, however, is a slime mold. As part of their lifecycle, the individual amoeba aggregate, forming a film, and then grow into a slug shape. (There are several other shapes that the aggregations take at various stages of the life cycle. Below are several slugs as well as a few other shapes.)

Scientists wanted to know how many individual amoeba cells go into a slug. To figure this out, they estimated the volume of an individual amoeba and the volume of a slug, then did arithmetic to find the number of amoeba in a slug.

In 1953, two scientists, Bonner and Frascella, estimated the diameter of a single Dictyostelium discoideum to be  (Remember that is one micrometer, or  They also measured the volume of a Dictyostelium discoideum slug. With these measurements, they estimated there are about amoeba in a single slug.

In 1998, Bonner returned to the problem and used new methods to estimate the diameter of a single amoeba. This time, he found for the average diameter. Bonner did not change his estimate of the volume of a slug between 1953 and 1998. He also didn't change his assumptions about the shape of amoeba, just the overall scale.

Bonner used his updated diameter measurement to re-estimate the number of amoeba in a single slug. What was his new estimate?

Jul 14, 2023

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In 1953, Bonner and Frascella estimated that the volume of a single amoeba was 4/3 * pi * (4 micrometer)^3 = 256 micrometer^3.

The volume of a slug was estimated to be 2.74 * 10^8 micrometer^3.

Therefore, the number of amoeba in a slug was estimated to be 2.74 * 10^8 / 256 = 105,000.

In 1998, Bonner estimated that the volume of a single amoeba was 4/3 * pi * (8 micrometer)^3 = 512 micrometer^3.

The volume of a slug was still estimated to be 2.74 * 10^8 micrometer^3.

Therefore, the number of amoeba in a slug was estimated to be 2.74 * 10^8 / 512 = 53,000.

So, Bonner's new estimate was 53,000 amoeba in a single slug.

Jul 14, 2023
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Sorry, that's incorrect...

flowiery  Jul 15, 2023