12.2 Surface Area of Prisms and Cylinders

Calculate the surface area of prisms and cylinders

1. Prisms and Cylinders
The student is able to (I can):
•Calculate the surface area of prisms and cylinders

2. The surface areais the total area of all faces and curved
surfaces of a three-dimensional figure. The lateral areaof a
prism is the sum of the areas of the lateral faces.
Let’s look at a net for a hexagonal prism:

3. The surface areais the total area of all faces and curved
surfaces of a three-dimensional figure. The lateral areaof a
prism is the sum of the areas of the lateral faces.
Let’s look at a net for a hexagonal prism:
What shape
do the
lateral faces
make?
(a rectangle)

4. If each side of the hexagon is 1 in., what is the perimeter of
the hexagon?
What is the length of the base of the big rectangle?
6 in.
6 in.

5. This relationship leads to the formula for the lateral area of a
prism:
L= Ph
where Pis the perimeter and his the height of the prism.
For the total surface area, add the areas of the two bases:
S= L+ 2B

6. A net of a cylinder looks like:
The length of the lateral surface is the circumference of the
circle, so the formula changes to:
L= Ch where C= dor 2r
and the formula for the total area is now:
S= L+ 2r
2

7. Examples: Find the lateral and total surface area of each.
1.
2.
10 cm
14 cm
4"3"
8"
5"

8. Examples: Find the lateral and total surface area of each.
1.
2.
10 cm
14 cm
4"3"
8"
5"
P= 3+4+5 = 12 in.
B= ½(3)(4) = 6 in
2
L= (12)(8) = 96 in
2
S= 96 + 2(6) = 108 in
2
C= 10cm
B= 5
2
= 25cm
2
L= (10)(14) = 140cm
2
S= 140+ 2(25)
= 190cm
2