6th Grade Math
Cylinder Task
a) Explain what is meant by surface area. What steps would you take to find the
surface area of a cylinder?
b) One of the major expenses in manufacturing a can is the amount of metal that
goes into it. How many square centimeters of metal would be required to
manufacture a can that has a diameter of 8 cm and a height of 20 cm?
Estimate and then solve.
c) Draw a net (pattern) for the manufacturer to use to make the can.
d) Use your work in parts a – c to write a rule in words for finding the surface area
of a cylinder. Now write your rule using letters, numbers, and mathematical
symbols (a formula).
e) Michael bakes a round two-layer birthday cake that is to be covered with
frosting on the top, sides, and in between the layers. Each layer has a height
of 4 cm and diameter of 24 cm. The label on the can of frosting he bought
claims that the contents will cover the top and sides of a one-layer rectangular
sheet cake that is 32 cm by 22 cm by 4 cm. Will Michael have enough
frosting? Show how you know.
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Cylinder Task
Discussion, Suggestions, Possible solutions:
This task deals primarily with the surface area of a right rectangular prism and a right circular
cylinder.
Parts a – d of this task may be used appropriately throughout the unit as an instructional
task. Part d could be used as a learning task or should the teacher prefer to divide this unit
into two smaller units, it may be used as a culminating task over surface area.
Georgia student work is available for this task.
a) Explain what is meant by surface area. What steps would you take to find the
surface area of a cylinder?
The surface area of a three dimensional figure is the sum of the areas of its faces. To find
the surface area of a cylinder, you would find the sum of the areas of the two circle bases
and the area of the rectangle that is wrapped around the circumference of those bases.
b) One of the major expenses in manufacturing a can is the amount of metal that
goes into it. How many square centimeters of metal would be required to
manufacture a can that has a diameter of 8 cm and a height of 20 cm? Estimate
and then solve.
To estimate the surface area of the can, one might think each circle has an area of a little
more than (3)(15) = 45cm2 and the rectangle would have an area of about (25)(20) =
500cm2. So a good estimate would be close to 600cm2.
To solve the problem, you would find the areas of the two circle bases which are (r2) each.
This would be (3.14 • 42) = 50.24cm2 each. Then to find the area of the rectangle, it would
be (circumference • height) or ( • d • h) which is (3.14 • 8 • 20) = 502.4. Therefore, the
surface area of the metal can would be 50.24 + 50.24 + 502.4 = 602.88cm2.
c) Draw a net (pattern) for the manufacturer to use to make the can.
d) Use your work in parts a – c to write a rule in words for finding the surface
area of a cylinder. Now write your rule using letters, numbers, and mathematical
symbols (a formula).
To find the surface area of a cylinder: find the areas of the two circles by doubling the
product of pi and the square of the radius, then and add the area of the rectangle which
would have a length of the circumference and a width that is the height of the cylinder. The
formula would be SA = 2(r2) + (d)(h) when SA= Surface Area of the cylinder, r = radius of
a circle base, d = diameter of a circle base, and h = height of the cylinder.
e) Michael bakes a round two-layer birthday cake that is to be covered with
frosting on the top, sides, and in between the layers. Each layer has a height of 4
cm and diameter of 24 cm. The label on the can of frosting he bought claims that
the contents will cover the top and sides of a one-layer rectangular sheet cake
that is 32 cm by 22 cm by 4 cm. Will Michael have enough frosting? Show how
you know.
Finding the area needed to ice the round cake:
Area of the top and middle = 2(r2)
= 2(3.14 • 122)
= 2(3.14 • 144)
= 2(452.16)
= 904.32c
Area of the side = (C)(h)
= (d)(h)
= (3.14 • 24)(2 • 4)
= (75.36)(8)
= 602.88cm2
The round cake will need to have enough icing to cover 904.32 + 602.88 = 1,507.2cm2.
Finding the area needed to ice the rectangular sheet cake:
Area of the top = lw
= (32)(22)
= 704cm2
Area of the front and back = 2(wh)
= 2(22)(4)
= 176cm2
Area of the left and right = 2(lh)
= 2(32)(4)
= 256cm2
The rectangular cake will need to have enough icing to cover 704 + 176 + 256 = 1,136cm2.
Michael will not have enough icing to frost the round cake because 1,507.2 is larger than
1,136.
Georgia student work is available for this task.
SIXTH GRADE MATHEMATICS GEORGIA STUDENT WORK SAMPLE:
Cylinder Task
f) Explain what is meant by surface area. What steps would you take to find the
surface area of a cylinder?
g) One of the major expenses in manufacturing a can is the amount of metal that
goes into it. How many square centimeters of metal would be required to
manufacture a can that has a diameter of 8 cm and a height of 20 cm?
Estimate and then solve.
h) Draw a net (pattern) for the manufacturer to use to make the can.
i) Use your work in parts a – c to write a rule in words for finding the surface area
of a cylinder. Now write your rule using letters, numbers, and mathematical
symbols (a formula).
j) Michael bakes a round two-layer birthday cake that is to be covered with
frosting on the top, sides, and in between the layers. Each layer has a height
of 4 cm and diameter of 24 cm. The label on the can of frosting he bought
claims that the contents will cover the top and sides of a one-layer rectangular
sheet cake that is 32 cm by 22 cm by 4 cm. Will Michael have enough
frosting? Show how you know.
M6N1. Students will understand the meaning of the four arithmetic operations as
related to positive rational numbers and will use these concepts to solve
problems.
g. Solve problems involving fractions, decimals, and percents.
M6M4. Students will determine the surface area of solid figures (right rectangular
prisms and cylinders).
a. Find the surface area of right rectangular prisms and cylinders using manipulatives and
constructing nets.
b. Compute the surface area of right rectangular prisms and cylinders using formulae.
c. Estimate the surface areas of simple geometric solids.
d. Solve application problems involving surface area of right rectangular prisms and
cylinders.
SIXTH GRADE MATHEMATICS GEORGIA STUDENT WORK SAMPLE:
Cylinder Task
a)
a)
1
2
b)
1) The student shows a clear
understanding
of the meaning of surface area.
2) The student demonstrates
that he/she is able to
determine the surface area of
a cylinder. (M6M4)
b)
3
3)Although the estimate of
the surface area of the cylinder is
reasonable, there no explanation
of the process. (M6M4c)
4
4) Even with a slight
computational error, it is evident
that the student does understand
the meaning of addition and
multiplication as related to
positive rational numbers and is
able to use these concepts to solve
problems. (M6N1)
c)
5
d)
6
e)
7
8
c)
5) It is apparent that the student
is able to construct a net for the
cylinder. (M6M4a)
d)
6) The work shown indicates
understanding of the development of the formula for surface
area of a cylinder. (M6M4)
e)
7) The computational error
mentioned in comment 4 is
corrected here.
8) All work is accurate and
indicates mastery of the standard
M6M4 and element M6M4d.
SIXTH GRADE MATHEMATICS GEORGIA STUDENT WORK SAMPLE:
Cylinder Task