Question

question 2
assume that a cell is a sphere with radius ( 10^{-3} ) or 0.001 centimeter, and that a cells density is 1.1 grams per cubic centimeter.
a. koalas weigh 6 kilograms on average. how many cells are in the average koala? type your answer... ( \times 10^{12} )
b. hippos weigh 1,400 kilograms on average. how many cells are in the average hippo? type your answer... ( \times 10^{14} )

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 \(
ho = 1.1\text{ g/cm}^{3}\)), \(m = 1.1\times\frac{4\pi}{3}\times10^{-9}\text{ g}\approx4.6\times10^{-9}\text{ g}\).

Step3: For koala (part a)

The mass of a koala \(M = 6\text{ kg}=6\times10^{3}\text{ g}\). The number of cells \(n=\frac{M}{m}=\frac{6\times 10^{3}}{4.6\times10^{-9}}\approx1.3\times10^{12}\).

Step4: For hippo (part b)

The mass of a hippo \(M = 1400\text{ kg}=1.4\times10^{6}\text{ g}\). The number of cells \(n=\frac{M}{m}=\frac{1.4\times 10^{6}}{4.6\times10^{-9}}\approx3.0\times10^{14}\).

Answer:

a. \(1.3\)
b. \(3.0\)