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Surface Area of a Cylinder

- Tim Carson
- Mary Ann Murphy
- Rebecca Mersereau
- Kate Peart

Teacher Reference

- Grade Level 8
- Unit Geometry
- SCO Students should be able to estimate and

calculate volumes and surface areas of right

prisms and cylinders. - Prior Knowledge Students should know how to

calculate the circumference and surface area of a

circle. They will also know how to calculate the

surface area of a rectangle and a rectangular

prism.

Setting the Stage

- Review the properties (circumference, radius,

etc.) of a circle - Review the area of a rectangle and circle
- Introduce and prepare the students for the

surface area of a cylinder - Define surface area

First Activity

- Use Transparency to review the properties of

circles and rectangles. - Review known formula for area with students.

Experimenting with Shapes and Area.

- Have students create pictures with shapes they

cut out from the handout. Then calculate the area

Area and Surface Area

- Definitions
- Area The measurement of the space inside the

perimeter of a 2-d object - Surface Area the sum of the area of each

individual surface of a 3-d object

Providing Context

- Problem Oh Henry has decided to create a new

chocolate bar in the shape of a cylinder. They

have made the chocolate bar to be 15 cm long and

3 cm in diameter. They now need to know how much

packaging they need to cover their first order of

100 bars.

Assessment Opportunity

- During the last 5 minutes of class have the

students write in their journals the answer to

the following question How would you go about

finding the answer to Oh Henrys problem?

Homework

- Have the students each bring in an example of a

cylinder from home. (ideally cans with the volume

marked on them) - However all cylinders are suitable.
- Provides context for a class discussion
- These will be used in the enrichment phase.

Core Discovery

- See Jodi MacInnis manip presentation
- http//people.stu.ca/7Epheeney/5873Manip_SurfaceA

reaCylinder.pdf

Core Discovery Alternative Option.

- The link below is to a movie on You Tube

demonstrating the same activity. Students who

need to see the demonstration again can use it

for follow up, or absent students can be directed

to this resource. - http//youtube.com/watch?vO5_7ymhemi0

Youtube video

Post Discovery.

- Reinforcement and Application
- Reinforce the formula for surface of the cylinder
- Apply the formula to various problems
- Determine the effect of changing the dimensions

of a cylinder on its surface area

Reinforcement

- Review the key principles from the manipulation

(teacher facilitates discussion) - Surface area depends on the radius of the base

and height of the cylinder - The width of the rectangle is the same as the

circumference of the circle. - Total surface area is the area of the top, bottom

and side.

Assessment Opportunity

- Demonstrate a couple sample questions from the

Find the Surface Area Overhead and have the

students complete selected questions from the

sheet before continuing. - See where common mistakes occur gives students

the opportunity to review or self reinforce the

concept of finding the surface area of a cylinder.

Word Problem

- Suppose you work for a company that makes water

tanks. A customer wants a tank that measures 10

meters in height and 3 meters in diameter. - How much metal should you order to make this

tank?

Revisit Context Question

- Oh Henry has decided
- to create a new chocolate
- bar in the shape of a
- cylinder. They have made
- the chocolate bar to be 15 cm long and 3 cm

in diameter. They now need to know how much

packaging they need to cover their first order of

100 bars. - After they figure out this out, ask if they have

any idea how to find out how much chocolate they

will need to make the chocolate bars.

Assessment Opportunity

- This asks students to apply their understanding

of the surface area of a cylinder and transform

the cylinder it also allows them to question the

surface area at different stages, make and

justify a hypothesis.

Post Discovery Enrichment

- Use the formula to derive the surface areas of

different geometric shapes - Compare the relationship between surface area and

volume

Brain Teaser?

- A cylinder 105 cm high has a circumference of 20

cm. A string makes exactly 7 complete turns round

the cylinder while its two ends touch the

cylinder's top and bottom. How long is the string

in cm?

Brain Teaser

- The figure alongside illustrates how the cylinder

can be unrolled into a rectangle for the case

where the string makes exactly 4 complete turns. - Since the students have not learned Pythagoreans

theorum formula they would be expected to measure

the length of the string with a ruler

Working with Cylinders

- Have the students get the cylinders that they

brought in and calculate the surface area of each

one. Having the students produce table similar to

the table provided below - Graph the total surface area against the volume

of the cylinder. Is there any relation between

the surface area and the volume

Confirming Knowledge

- As a reinforcement, this website allows students

to manipulate the dimensions of rectangular and

triangular prism to obtain the same relationships

Assessment Opportunity

- After completing the graph of the relationship

between surface area and volume of a cylinder

students are given the opportunity to look at

squares and Triangular prisms. - This can provide a discussion opportunity for

students to share what they have learned.

Show You Know

- For 5-7 minutes, have them in their groups

discuss what might be a possible solution to the

problem and then work it out. After the groups

have finished, have students present their

solution to the class and discuss why each

solution is either right or wrong. Have them do

this using only the symbols not with numbers.

Assessment Opportunity

- Within the groups students will be discussing the

model of the square with a cylindrical hole. They

will be using the formula they know for

rectangular prisms also what they have been

learning for cylinders. The formulas the groups

come up will help inform the teacher of their

understanding of the concept.

Thank You

- Questions/ Comments?

References

- http//id.mind.net/zona/mmts/geometrySection/surf

aceAreasAndVolumes/areaVolumeBoxCylindricalHole1.h

tml - http//www.syvum.com/cgi/online/serve.cgi/contrib/

teasers/string1.tdf?0 - http//illuminations.nctm.org/Lessons/Scaling/Scal

ing-AS-ScalingAway.pdf - http//www.purplemath.com/modules/perimetr.htm
- http//www2.whidbey.net/ohmsmath/webwork/javascrip

t/prismcyl.htm - http//youtube.com/watch?vO5_7ymhemi0
- http//www.math.wichita.edu/history/activities/geo

metryact.htmlareavolume-act - http//www.math.wichita.edu/history/activities/geo

metryact.htmlareavolume-act

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