Goal: Students will develop a formula for the surface area of a sphere on their own.
Objectives: Through the use of collected data and prompting from the teacher, students will use the characteristics of an orange to create a formula for the surface area of a sphere.
Vocabulary: Surface area: the total area of the surface of a three dimensional object Radius: a line segment that joins the center of the sphere with any point on its surface Circumference: the distance around the edge of a circle Great circle of a sphere: the exposed circle of a sphere when it is cut in half.
How do these definitions relate to an orange?
Procedure:
1.Cut oranges in half and distribute to pairs/groups of students.
2. According to the orange, record your ideas regarding: What is the radius? _______________________________________________________ What is the great circle of a sphere? _________________________________________ What is the circumference? ________________________________________________ What is the surface area? __________________________________________________
3.Trace your great circle onto a piece of paper. If you were to peel the orange and place the pieces into a circle this size, how many circles would the pieces fit into? Take a guess. ________________________________________________________________________
4. Trace 5 or 6 circles onto your paper and start peeling your orange. Make sure the pieces are small enough to line up next to each other nicely. Try not to leave space in between and no pieces can overlap.
5. How many circles did your peels fill? ________ Was your prediction correct? _________
6.Think about how you can determine the surface area of your orange. Measure the circumference of the circles you traced with the string and ruler. Can you use this data to figure out the surface area? Use the space below to do some calculations. *Hint: You may want to use the formula for area of a circle here.
7. What is the surface area of your orange? ________________________________________
8. Can you create a formula that determines the surface area of the orange? ________________________________________________________________________
9.Do you think that your formula can be used to find the surface area of any sphere? Explain why or why not. ______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________