|Surface Areas and Volumes of Spheres
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.
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.
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
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?)
Present the formulae for calculating surface area and volume of sheres:
Demonstrate the use of Microsoft Excel and the process of building formulae.
Direct each student
to create a spreadsheet with the following columns:
Demonstrate how to
make a line graph with the data.
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.
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
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
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 ___
(link to your school's homepage if you have one.)