2. 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.

3. Lateral Edges
Bases Lateral Faces
Bases
Triangular
Pentagonal Prism
Prism
h h
Right Prism Oblique Prism

4. Lateral Area and Surface Area of a Prism
Base Perimeter
h
L = Ph
Lateral Base Height
Area Perimeter
Base Area
S = L + 2B
Surface Lateral Base Area
Area Area

5. Find the surface area of the regular hexagonal
prism.
S = L + 2B
L = Ph 1 P = 36
L = 432 m B = 2 .5
B = 93apm 2
2
P = 6(6) = 36
S = 432 + 2(93.5)
1
( )
12 m
L = 36(12) B = 3 3 ( 36 )
6m
360 60
S = 432 + 187 2 6
= = 30
2
L = 432 m 2
30
S = 619 m B = 54 3
2 3 3m
B = 93.5 m 2 3m
60

6. Find the surface area of the
triangular prism.
S = L + 2B
1
L = Ph B = bh 12 cm
2
L = 16(12) B = 0.5(6)(4) 5 cm 6 cm
P = 16
L = 192 cm 2
B = 12 cm 2 5 cm
32 + h 2 = 5 2
S = 192 + 2(12) 5 cm
9 + h 2 = 25
h
h 2 = 16
S = 216 cm 2
3 cm
h=4

7. Lateral Area and Surface Area of a Cylinder
L = 2πrh
Base Area
Radius
Lateral Radius Height
h Area
S = L + 2B
Surface
Area
Lateral
Area B = πr
Base Area 2

8. Find the surface area of a cylinder with 5 cm
height 10 cm and radius 5 cm in terms of
pi.
10 cm
S = L + 2B
L = 2πrh B = πr 2
L = 2π (5)(10) B = π (5) 2
L = 100π cm 2
B = 25π cm 2
S = 100π + 2(25π ) S = 150π cm 2

9. Find the surface area of a cylinder with
radius 6 ft and height 9 ft in terms of pi.
9 ft
S = L + 2B
L = 2πrh B = πr 2 6 ft
L = 2π (6)(9) B = π ( 6) 2
L = 108π ft 2
B = 36π ft 2
S = 108π + 2(36π ) S = 180π ft 2

10. Find the surface area of a cylinder with
radius 6 ft and height 9 ft in terms of pi.
9 ft
S = L + 2B
L = 2πrh B = πr 2 6 ft
L = 2π (6)(9) B = π ( 6) 2
L = 108π ft 2
B = 36π ft 2
S = 108π + 2(36π ) S = 180π ft 2