Surface Areas and Volumes of Spheres
 
Jashan Blackwell
Introduction
Standards 
Objectives
Activities
Assessment 
Results
Resources
.
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.

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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 =4pr2
V =4/3pr3
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 (ft3) Surface Area (ft2) 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 Sub-task 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 pre-test, post-test, and culminating assessment data.
Surface Areas and Volumes of Spheres
Lesson 11.6

Pre-test
 

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
 
 


 
 
 
 
 
 
 
 
 
 
 
 
 
 

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Last Revised: 06/30/2000 (insert and update last revision date every time you work on this page.)