Question

Suppose the cells of a tumor are idealized as spheres each with a radius of 5 mum ​(micrometers). The number of cells has a doubling time of 35 days. Approximately how long will it take a single cell to grow into a​ multi-celled spherical tumor with a volume of 0.2 cmcubed ​(1 cmequals​10,000 mu​m)

Answer 1

Answer:

1044.3 days

Explanation:

Given,

Radius of sphere shaped cells of tumor $= 5$ micrometer

$1$ centimeter $= 10,000$ micrometers

Thus, radius of sphere in centimeters

$= \frac{5}{10,000}$

Volume of a sphere

$= \frac{4}{3} \pi r^{3}$

Volume of one cell of tumor

$\frac{4}{3} *(3.14)*(\frac{5}{10,000})^{3}\\= {5.23 * 10^{-10}$ centimeter cube

As we know ,

$N(t) = N(0) e^{-kt}\\\\k = \frac{ln2}{35}\\ k = 0.0198 day^{-1}$

Substituting all the given values in above equation, we get -

$0.2 = 5.23 * 10^{-10} * e^{-0.0198*t}\\t = 1044.3$ days