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Lanier Middle School
“An International Baccalaureate Middle Years Programme School”
8th – LESSON 10.1 Surface Area of Prisms
Daily Objective: How do you find the surface area of a cylinder?
Just as you did with a prism, you can use a net to help you find a
formula for the surface area of a cylinder.
The lateral area of a cylinder is the area of the curved surface that
connect the two bases. The net shows that the lateral surface is a
rectangle.
Example
Find the lateral and total surface are of the cylinder. Use
3.14 for pi and round your answer to the nearest tenth.
Draw a net in your notebook with all the dimensions
labeled.
Example
Find the lateral and total surface area of the cylinder.
Use 3.14 for pi and round your answer to the nearest
tenth. Draw a net in your notebook with all the
dimensions labeled.
Use the diagram of the oatmeal container and its net.
Imagine unrolling the container’s lateral surface to form a
rectnagle.
What dimension of the cylinder matches the rectangle’s length?
Lateral Area =
Example
The can shown is 11 inches high and has a diameter of 9
inches. How many square inches of paper are needed for
the label? How many square inches of metal area
needed to make the entire can? Round your answers t
othe nearest whole number. Use 3.14 for pi. Draw a net
in your notebook with all the dimensions labeled.
Total Surface Area =
Example
How many square inches of cardboard are needed for the
latteral area of the raisin container shown? What is the
total surface area of the container? Round your answers
to the nearest tenth. Use 3.14 for pi. Draw a net in your
notebook with all the dimensions labeled.
Lanier Middle School
“An International Baccalaureate Middle Years Programme School”
1
Draw a net of the cylinder. Label the radius and the height. Then
find the lateral area and total surface area. Round your answers
to the nearest tenth. Use 3.14 for pi. Draw a net in your
notebook with all dimensions labeled.
For the next problems find the lateral and total surface area of
each cylinder. Round your answers to the nearest tenth.
Use 3.14 for pi. Draw a net in your notebook with all dimensions
labeled.
4
5
6
2
A can of tuna fish has a height of 1 inch and a diameter of
3 inches. How many square inches of paper are needed
for the label? How many square inches of metal are
needed to make the can including the top and bottom?
Round your answers to the nearest whole number. Use
3.14 for pi. Draw a net in your notebook with all
dimensions labeled.
7
A container of bread crumbs has a radius of 4 inches and
a height of 8 inches.
8
A rain barrel has a diameter of 18 inches and a height of 3
feet.
10
A pipe is 25 inches long and has a diameter of 5 inches. What is
the lateral area of the pipe to the nearest tenth? Use 3.14 for pi.
Make a diagram of the pipe and its net in your notebook with all
dimensions labeled.
11
A size D battery has a diameter of 32 millimeters and a length of
5.6 centimeters. What is the lateral area of the battery to the
nearest square centimeter? Use 3.14 for pi.
15
The treasure chest shown is a composite figure. What is the
surface area of the treasure chest to the nearest square foot?
16
A square prism has the same height as the cylinder shown. The
perimeter of the prism’s base equals the circumference of the
cylinder’s base. Which figure has the greatest lateral area, total
surface area, and volume?
9
A drum has a diameter of 14 inches and a height of 5.5
inches.
12
Carol is designing an oatmeal container. Her first design
is a rectangular prism with a height of 12 inches, a width
of 8 inches, and a depth of 3 inches.
What is the total surface area of the container to the
nearest square inch?
Carol wants to redesign the package as a cylinder with
the same total surface area as the prism. If the radius of
the cylinder is 2 inches, what is the height of the
cylinder? Round your answer to the nearest inch. Use
3.14 for pi.
17
A cylinder has a circumference of 16 inches and its
height is half of the radius of the cylinder. What is the
total surface area of the cylinder? Give your answer in
terms of  .
Lanier Middle School
“An International Baccalaureate Middle Years Programme School”