MATHEMATICS · Multi-part · CBSE · Mathematics · Power Play · Power Play
Problem
For a quick health-related project, a student wishes to estimate how many skin cells cover her body. Assume the student is 1.60m tall and can be approximated by simple geometric shapes as instructed below. The average skin cell is roughly square with side 30μm.
Carry out the estimation by answering all parts.
(i) Choose a convenient geometric model for the student’s torso, arms and legs, clearly stating every assumption you make about lengths, radii or widths.
(ii) Using your assumptions, compute an approximate total surface area of the student’s skin (face, neck, hands and feet may be treated together with the main surfaces as a single area figure).
(iii) From the surface area obtained in part (ii), estimate the total number of skin cells on the student’s body and express the result in scientific notation, keeping two significant figures.
(iv) Comment briefly on one main source of uncertainty in your estimate and how it might change the final order of magnitude result.