Introduction
This lesson provides an opportunity for students
to use spreadsheet software to calculate the surface areas and volumes
of spheres and to graph their relationship as a function of radius.
Geometry
Topic: Surface Areas and Volumes of Spheres
Grade Level: High School
Student Lesson name and URL:
Standards
Addressed
High School
Math: Focus on Geometry
Surface Area and Volume
of Spheres
9.0 Students compute the volumes and surface areas of prisms,
pyramids, cylinders, cones and spheres; and students commit to memory the
formulas for prisms, pyramids and cylinders.
.
Instructional
Objectives
Given 5 different values for
the radius of a sphere, the student will calculate the surface area and
volume using spreadsheet software. The student will then create graphs
of Volume, surface area and their ratio as a function of radius.
Student
Activities
Introductory
Activity
Give each student
a balloon to inflate, a ruler and a piece of string. Have each student
inflate his/her balloon and then estimate the radius and circumference
using the ruler and string. Then ask them to examine the relationship
between radius and circumference and express it as a formula. Once
they have completed that task, ask them to predict the effect of radius
on volume and surface area (how big is the balloon and how much air did
you put in it?)
Enabling
Activity(ies)
Present the formulae
for calculating surface area and volume of sheres:
SA =4pr^{2}
V =4/3pr^{3}
Demonstrate the
use of Microsoft Excel and the process of building formulae.
Direct each student
to create a spreadsheet with the following columns:
Radius (ft) 
Volume (ft^{3}) 
Surface Area (ft^{2}) 
Volume/Surface Area 
1 
=4/3x3.14x(R2C1)^{3} 
=4x3.14x(R2C1)^{2} 
=R2C2/R2C3 
2 



3 



4 



5 



Demonstrate how to
make a line graph with the data.
Have each student
graph the relationship between column1 and each of the other columns.
Ask them what they
discovered.
Have each student
use an internet search engine to find the radius of each of the planets
in the solar system. Have students enter the radii of planets in
the speadsheet and calculate their volumes and surface areas. Ask
students to compare their answers with the numbers found for their sample
spheres.
Culminating
Activity
Have students print
their spreadsheets and review the formulae for calculating volume and surface
area. Ask students to review and interpret their graphs and present
their findings to the class.
Assessment
Grading Rubric
Task 
Subtask 
Outstanding 
Satisfactory 
Unsatisfactory 
Spreadsheet Built 
Volume 




Surface Area 




Volume/Surface Area 



Graph Complete 
Volume 




Surface Area 




Volume/Surface Area 



Web Search 
Planets 



Presentation 
Printed Materials 




Oral Clarity 



Results
After implementing your lesson
(sometime between January & March), insert a chart of your pretest,
posttest, and culminating assessment data.
Surface Areas and Volumes
of Spheres
Lesson 11.6
Pretest
1) What is the relationship
between radius and volume of spheres?
___________________________________________________
2) What is the relationship
between radius and Surface area of spheres?
___________________________________________________
3) What is the relationship
between radius and the ratio of Volume to Surface area of spheres?
___________________________________________________
4) Can you build a spreadsheet
in Excel? Yes ___ No ___
5) Can you use formulae in
Excel?
Yes ___ No ___
6) Do you know how to graph
data from an Excel spreadsheet?
Yes
___ No ___
7) Can you use an Internet
search engine to find information on the Internet?
Yes ___ No ___
Web
Resources & Supplementary Materials
Enabling Activity
Two useful sites for information
about the planets
http://pds.jpl.nasa.gov/planets/welcome.htm
http://www.seds.org/nineplanets/nineplanets/nineplanets.html
School Name
(link to your school's homepage if you have one.)
School
Location
Your Name
and email address
Last Revised:
06/30/2000 (insert and update last revision date every time you
work on this page.) 