Chapter 1, Problem 32P

Treat a cell in a human as a sphere of radius 1.0 μm. (a) Determine the volume of a cell. (b) Estimate     the volume of your body. (c) Estimate the number of cells in your body.

To determine

The volume of the cell.

Answer to Problem 32P

The volume of the cell is $4.2\times {10}^{-18}{\text{m}}^{\text{3}}$

Explanation of Solution

Given Info: The radius of spherical cell is $1\times {10}^{-6}\text{m}$.

Explanation:

Formula to calculate the volume of the spherical cell is,

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

• $V_{cell}$ is volume of the spherical cell,
• $r$ is radius of the spherical cell

Substitute $1\times {10}^{-6}\text{m}$ for $r$ to find $V_{cell}$.

$\begin{array}{c}{V}_{cell}=\frac{4}{3}\pi {\left(1\times {10}^{-6}\text{m}\right)}^3\\ =4.2\times {10}^{-18}{\text{m}}^3\end{array}$

Thus, volume of spherical cell $\left(V_{cell}\right)$ is $4.2\times {10}^{-18}{\text{m}}^3$

Conclusion:

Therefore, the volume of spherical cell $\left(V_{cell}\right)$ is $4.2\times {10}^{-18}{\text{m}}^3$

To determine

The volume of the human body.

Answer to Problem 32P

The volume of the human body is $1\times {10}^{-1}{\text{m}}^{\text{3}}$

Explanation of Solution

Considered the human body as a cylindrical shape which is having radius about $0.15\text{m}$ and height of about $1.5\text{m}$

Formula to calculate the volume of the cylindrical body is,

$V_{body}=\pi r^{2}h$

• $V_{body}$ is volume of the body,
• $r$ is radius of the cylindrical body
• $h$ is the height of the cylindrical body

Substitute $0.15\text{m}$ for $r$, $1.5\text{m}$ for $h$ to find $V_{body}$.

$\begin{array}{c}{V}_{body}=\pi {\left(0.15\text{m}\right)}^2\left(1.5\text{m}\right)\\ =0.11{\text{m}}^3\\ \approx 1\times {10}^{-1}{\text{m}}^{\text{3}}\end{array}$

Thus, volume of cylindrical body $\left(V_{body}\right)$ is $1\times {10}^{-1}{\text{m}}^3$

Conclusion:

Therefore, the volume of cylindrical body $\left(V_{body}\right)$ is $1\times {10}^{-1}{\text{m}}^3$

To determine

The number of cell in body.

Answer to Problem 32P

The number of cell in body is $\sim {10}^{16}$

Explanation of Solution

Formula to calculate the number of cell in body is,

$n=\frac{V_{body}}{V_{cell}}$

• $V_{body}$ is volume of the body,
• $V_{cell}$ is volume of cell
• $n$ is the number of cell in body

Substitute $1\times {10}^{-1}{\text{m}}^3$ for $V_{body}$, $4.2\times {10}^{-18}{\text{m}}^3$ for $V_{cell}$ to find $n$.

$\begin{array}{l}n=\frac{\left(1\times {10}^{-1}{\text{m}}^{\text{3}}\right)}{\left(4.2\times {10}^{-18}{\text{m}}^{\text{3}}\right)}\\ =2.6\times {10}^{16}\\ \approx {10}^{16}\end{array}$

Thus, number of cell in body $\left(n\right)$ is $\approx {10}^{16}$

Conclusion:

Therefore, the number of cell in body $\left(n\right)$ is $\approx {10}^{16}$