Question

Make a rough estimate of the volume of your body (in${\mathrm{m}}^3$).

Short answer

The volume of your body is approximately $8\times {10}^{-2}{\mathrm{m}}^3$.

Step-by-step solution

Step 1. Definition of a rough estimate

A rough estimate is an approximate calculation of a quantity or a number.

Step 2. Definition of volume

Volume is defined as the amount of space occupied by a solid 3-D figure like a cuboid, cylinder, or sphere.

Step 3. Assumptions to determine the volume of a human body

Assume that your body is a perfect cylinder with the dimensions corresponding to your body (tall and approx. 30-inch waist).

Thus, the cross-sectional radius (r) will be $0.12\mathrm{m}$.

The height (h) of the cylinder will be $1.70\mathrm{m}$.

Step 4. Determination of the volume of the cylinder

The volume of a regular cylinder is $V=\pi r^{2}h$.

Substitute the numerical values in the above expression.

$\begin{array}{c}V=3.14{\left(0.12\mathrm{m}\right)}^2\left(1.70\mathrm{m}\right)\\ =0.07690{\mathrm{m}}^3\\ \approx 8\times {10}^{-2}{\mathrm{m}}^3\end{array}$

Thus, the volume of the body is roughly $8\times {10}^{-2}{\mathrm{m}}^3$.