CM L3 Health in Maths
Body Surface Area (BSA)
Task 1a
Your challenge is to estimate the body surface area of someone in your group.
First make an estimate of the person’s body surface area by observing them.
Now make a second estimate and use the following tools to help you, toilet
rolls, flip chart paper, A3- A4 paper, plastic bags or any other way that you can
think of.
Developed and adapted by Martin Newton @ Stoke on Trent College, early adopters with Core
Maths Support programme, based on an idea from NCETM MEP follow up session
CM L3 Health in Maths
Task 1b
There are other ways of working out the body’s surface area.
One way involves using the formulae of mathematical shapes.
Estimate using solids as above and compare to your original estimate and the
estimate using toilet rolls and paper.
Developed and adapted by Martin Newton @ Stoke on Trent College, early adopters with Core
Maths Support programme, based on an idea from NCETM MEP follow up session
CM L3 Health in Maths
Task 1b
Surface Area Formulae
Cylinder
SA = 2πrh + 2πr2
Cone
SA = πr2 + πrl
Sphere
SA = 4πr2
Developed and adapted by Martin Newton @ Stoke on Trent College, early adopters with Core
Maths Support programme, based on an idea from NCETM MEP follow up session
CM L3 Health in Maths
Task 1c
Body Surface Area Formula (Mosteller formula)
Another way of calculating BSA involves using Mostellar’s formula, a formula
used by medical staff to help them work out the correct drug dosage to give a
patient when the medicine depends on the body’s surface area eg
chemotherapy.
Body Surface Area (m2 ) =
Height (cm) x Weight (kg)
3600
Use Mosteller’s formula to calculate body surface area, how close were you
using the previous estimates?
Another formula used to calculate body surface area is the DuBois and DuBois
formula
The DuBois and DuBois formula2
BSA (m2) = 0.20247 x Height(m)0.725 x Weight(kg)0.425
Developed and adapted by Martin Newton @ Stoke on Trent College, early adopters with Core
Maths Support programme, based on an idea from NCETM MEP follow up session
CM L3 Health in Maths
Use the DuBois formula and compare to Mosteller.
Use the Mosteller formula to compare to DuBois for all the members of your
group.
Task 1d
Use a scatter diagram to compare Mostellors and DuBois formulas for the
whole class. State if there is a relationship and correlation between the two
formulas, from this does it matter which formula you would use? Use graph
paper
Developed and adapted by Martin Newton @ Stoke on Trent College, early adopters with Core
Maths Support programme, based on an idea from NCETM MEP follow up session
CM L3 Health in Maths
Investigate further:
Pearson's Correlation Coefficient
Correlation is a technique for investigating the relationship between two
quantitative, continuous variables, for example, age and blood pressure.
Pearson's correlation coefficient (r) is a measure of the strength of the
association between the two variables.
The first step in studying the relationship between two continuous variables is
to draw a scatter plot of the variables to check for linearity. The correlation
coefficient should not be calculated if the relationship is not linear. For
correlation only purposes, it does not really matter on which axis the variables
are plotted. However, conventionally, the independent (or explanatory)
variable is plotted on the x-axis (horizontally) and the dependent (or response)
variable is plotted on the y-axis (vertically).
The nearer the scatter of points is to a straight line, the higher the strength of
association between the variables. Also, it does not matter what measurement
units are used.
Values of Pearson's correlation coefficient
Pearson's correlation coefficient (r) for continuous (interval level) data ranges
from -1 to +1:
r = -1
data lie on a perfect straight line with a
negative slope
Developed and adapted by Martin Newton @ Stoke on Trent College, early adopters with Core
Maths Support programme, based on an idea from NCETM MEP follow up session
CM L3 Health in Maths
r=0
no linear relationship between the variables
r = +1
data lie on a perfect straight line with a
positive slope
Positive correlation indicates that both variables increase or decrease
together, whereas negative correlation indicates that as one variable increases,
so the other decreases, and vice versa.
Developed and adapted by Martin Newton @ Stoke on Trent College, early adopters with Core
Maths Support programme, based on an idea from NCETM MEP follow up session
CM L3 Health in Maths
Computing the Pearson Correlation Coefficient
One formula for the Pearson correlation coefficient r is as follows:
(10.1)
The following numerical example shows how the formula ( 10.1) is used:
Developed and adapted by Martin Newton @ Stoke on Trent College, early adopters with Core
Maths Support programme, based on an idea from NCETM MEP follow up session
CM L3 Health in Maths
Use Pearsons to see if there is any correlation between the two formulas?
Developed and adapted by Martin Newton @ Stoke on Trent College, early adopters with Core
Maths Support programme, based on an idea from NCETM MEP follow up session
CM L3 Health in Maths
Task 1e
Health questions in context:
Average BSAs for children of various ages, for men, and for women, are taken
to be:
Neonate (newborn)
Child of 2 years
9 years
10 years
12–13 years
Women
Men
0.25 m²
0.5 m²
1.07 m²
1.14 m²
1.33 m²
1.6 m²
1.9 m²
1. Using Mostellers formula find the BSA of a male cancer patient that is
180cm tall and weighs 75kg. Calculate the percentage difference with
average BSA for men.
2. Use the DuBois and DuBois formula to calculate the body surface area of
a 10 year old child who weighs 70lbs and is 4ft 7inchs. What is the
percentage difference between the average BSA and the child’s BSA?
3. A male patient’s BSA using Mosteller’s formula was calculated to be
2.1236, his height is 1.91m. Rearrange Mosteller’s to find the patients
weight.
4. Another way of working out body surface area is to use a table. Use the
BSA table to work out BSA for a person whose height is 1.65m and
weighs 47kg. Do the same for the following people, Haleema, 1.7m,
51kg; Jordan, 188cm, 73kg, Dale, 95kg, 1.82m
Developed and adapted by Martin Newton @ Stoke on Trent College, early adopters with Core
Maths Support programme, based on an idea from NCETM MEP follow up session
CM L3 Health in Maths
5. Using tables find the weight of a person that is 159cm tall and has a BSA
of 1.99. Give their height and weight using imperial measurements.
6. Set up a spreadsheet to use Mosteller’s and DuBois formulas, use this to
check all the calculations that you have done in all of the tasks.
Developed and adapted by Martin Newton @ Stoke on Trent College, early adopters with Core
Maths Support programme, based on an idea from NCETM MEP follow up session