1. Surface Areas of Prisms & Cylinders
Section 11-2

2. Objectives To find the surface area of a prism
To find the surface area of a cylinder

3. All About Prisms
Prism - a polyhedron w/ exactly 2 congruent, parallel faces, called bases.
Lateral faces - the faces that are not bases in a polyhedron
Named by the shape of its bases
Altitude - perpendicular segment that joins the planes of the bases
Height (h) - length of the altitude

5. Vocab Ctd. Lateral area - the sum of the areas of the lateral faces
Surface area - the sum of the lateral area and area of the two bases

6. Use a net to find the surface area of the cube.
Draw a net for the cube.
Find the area of one face. 112 = 121
The area of each face is 121 in.2.
Surface Area = sum of areas of lateral faces + area of bases
= ( ) + ( )
= 6 • 121
= 726
Because there are six identical faces, the surface area is 726 in.2.

7. You try
Use a net to find the S.A. of the triangular prism

8. Formulas

9. Use the formula L.A. = ph to find the lateral area and the formula
Find the surface area of a 10-cm high right prism with triangular bases having 18-cm edges. Round to the nearest whole number.
Use the formula L.A. = ph to find the lateral area and the formula
S.A. = L.A. + 2B to find the surface area of the prism. The area B of the base is ap, where a is the apothem and p is the perimeter. 1 2
The triangle has sides of length 18 cm, so p = 3 • 18 cm, or 54 cm.
Draw the base.
Use 30°-60°-90° triangles to find the apothem.

10. 9 = 3  a longer leg  3  shorter leg
(continued)
9 =  a longer leg   shorter leg
9 3 3 9
a =  = = Rationalize the denominator.
B = ap =   54 = 1 2
The area of each base of the prism is cm2.
S.A. = L.A B Use the formula for surface area.
= ph + 2B
= (54)(10) + 2( ) Substitute =
Use a calculator.
Rounded to the nearest whole number, the surface area is 821 cm2.

11. You try
Use formulas to find L.A. & S.A. of the prism

13. All About Cylinders Has 2 congruent parallel bases, which are circles.
Altitude - perpendicular segment that joins the planes of the bases
Height - length of the altitude
L.A. - area of resulting rectangle that can be formed by unrolling the cylinder
S.A. - sum of the lateral area & area of bases

16. The radius of the base of a cylinder is 6 ft, and its height is 9 ft
The radius of the base of a cylinder is 6 ft, and its height is 9 ft. Find its surface area in terms of .
S.A. = L.A B Use the formula for surface area of a cylinder.
= rh + 2( r 2) Substitute the formula for lateral area of a cylinder and area of a circle.
= (6)(9) (62) Substitute 6 for r and 9 for h.
= Simplify.
= 180
The surface area of the cylinder is ft2.

17. You try
Find the S.A. of a cylinder with a height of 10cm and radius of 10cm in terms of pi.
400cm2

18. Use the formula for surface area of a cylinder.
A company sells cornmeal and barley in cylindrical containers. The diameter of the base of the 6-in. high cornmeal container is 4 in. The diameter of the base of the 4-in. high barley container is 6 in. Which container has the greater surface area?
Find the surface area of each container. Remember that r = . d 2
S.A. = L.A B
Cornmeal Container Barley Container
Use the formula for surface area of a cylinder.
= rh r 2
Substitute the formulas for lateral area of a cylinder and area of a circle.

19. surface area of a cylinder.
(continued)
Cornmeal Container Barley Container
S.A. = L.A B
Use the formula for
surface area of a cylinder.
S.A. = L.A B
= rh r 2
Substitute the formulas for lateral area of a cylinder and area of a circle.
= rh r 2
= (2)(6) (22 )
= (3)(4) (32 )
Substitute
for r and h. = =
Simplify.
= 32
= 42
Because in.2  in.2, the barley container has the greater surface area.