Students compute the volumes and surface areas of prisms, pyramids, cylinders, cones, and spheres; and students commit to memory the formulas for prisms, pyramids, and cylinders.

Pentagonal Prism

Triangular Prism

Lateral Faces

Lateral Edges

BasesBases

Oblique Prism

h

Right Prism

h

Lateral Area and Surface Area of a Prism

PhL =Lateral Area

Base Perimeter

Height

BLS 2+=Surface

AreaLateral Area

Base Area

Base Perimeter

h

Base Area

Find the surface area of the regular hexagonal prism.

12 m6 m

PhL =)6(6=P 36=

BLS 2+=apB

2

1=

)12(36=L2m 432=L 30

60m 3

m 33

( )( )36332

1=B

354=B2m 5.93=B

2m 432=L 2m 5.93=B)5.93(2432 +=S

187432 +=S2m 619=S

=6

360 =2

6030

P = 36

Find the surface area of the triangular prism.

12 cm

5 cm

5 cm 6 cm

BLS 2+=

PhL = bhB2

1=

)12(2192 +=S2cm 216=S

5 cm

3 cm

222 53 =+ h

h 259 2 =+ h162 =h

4=h

)12(16=LP = 162cm 192=L

)4)(6(5.0=B2cm 12=B

Lateral Area and Surface Area of a Cylinder

rhL π2=Lateral Area

Radius Height

BLS 2+=Surface

AreaLateral Area

Base Area

Radius

h

Base Area

2rB π=

Find the surface area of a cylinder with height 10 cm and radius 5 cm in terms of pi.

10 cm

5 cm

rhL π2=BLS 2+=

)10)(5(2π=L2cm 100π=L

2rB π=2)5(π=B

2cm 25π=B)25(2100 ππ +=S 2cm 150π=S

Find the surface area of a cylinder with radius 6 ft and height 9 ft in terms of pi.

9 ft

6 ftrhL π2=BLS 2+=

)9)(6(2π=L2ft 108π=L

2rB π=2)6(π=B

2ft 36π=B)36(2108 ππ +=S 2ft 180π=S

Find the surface area of a cylinder with radius 6 ft and height 9 ft in terms of pi.

9 ft

6 ftrhL π2=BLS 2+=

)9)(6(2π=L2ft 108π=L

2rB π=2)6(π=B

2ft 36π=B)36(2108 ππ +=S 2ft 180π=S