Question

1. assume that a cell is a sphere with radius $10^{-3}$ or 0.001 centimeter, and that a cell’s density is 1.1 grams per cubic centimeter.

a. koalas weigh 6 kilograms on average. how many cells are in the average koala?
b. hippos weigh 1,400 kilograms on average. how many cells are in the average hippo?
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Explanation:

Step1: Calculate the volume of a cell

The volume formula for a sphere is \(V=\frac{4}{3}\pi r^{3}\). Given \(r = 10^{-3}\text{ cm}\), then \(V=\frac{4}{3}\pi(10^{-3})^{3}=\frac{4\pi}{3}\times10^{-9}\text{ cm}^{3}\)

Step2: Calculate the mass of a cell

Using the formula \(m=
ho V\) (where \(
ho = 1.1\text{ g/cm}^{3}\)), \(m = 1.1\times\frac{4\pi}{3}\times10^{-9}\text{ g}\approx4.618\times10^{-9}\text{ g}\)

Step3: Convert the mass of the koala to grams

Since \(1\text{ kg}=1000\text{ g}\), for a \(6\text{ kg}\) koala, its mass \(M = 6\times1000=6000\text{ g}\)

Step4: Calculate the number of cells in the koala

The number of cells \(n=\frac{M}{m}=\frac{6000}{4.618\times 10^{-9}}\approx1.3\times10^{12}\)

Step5: Convert the mass of the hippo to grams

For a \(1400\text{ kg}\) hippo, its mass \(M'=1400\times1000 = 1400000\text{ g}\)

Step6: Calculate the number of cells in the hippo

The number of cells \(n'=\frac{M'}{m}=\frac{1400000}{4.618\times10^{-9}}\approx3.03\times10^{14}\)

Answer:

a. Approximately \(1.3\times 10^{12}\) cells.
b. Approximately \(3.03\times 10^{14}\) cells.