1. Lesson 12-3, 4, 13-1
Cylinders
&
Prisms

2. Objectives Find lateral areas of cylinders
Find surface areas of cylinders
Find volume of cylinders
Find lateral areas of prisms
Find surface areas of prisms
Find the volume of prisms

3. Vocabulary
Axis of a Cylinder – the segment with endpoints that are centers of circular bases
Right Cylinder – A cylinder where the axis is also an altitude
Oblique Cylinder – a non-right cylinder
Bases – congruent faces in parallel planes
Lateral faces – rectangular faces that are not bases (not all parallel)
Lateral edges – intersection of lateral faces
Right Prisms – a prism with lateral edges that are also altitudes
Oblique Prisms – a non-right prism
Lateral Area – is the sum of the areas of the lateral faces

4. Cylinders – Surface Area & Volume
r – radius
h – height
Net h h r C
Volume (V) = B * h
Base Area (B) = π * r2
V = π * r2 * h
Surface Area = Lateral Area + Base(s) Area
LA = 2π • r • h = circumference * h
Bases Area = 2 • π • r2
SA = LA + BA
SA = 2π • r • h + 2π • r² = 2πr (r + h)

5. Example 1 12 3
Find the surface area and the volume of the cylinder to the right
SA = 2πrh + 2πr2  need to find r and h
SA = 2πrh + 2πr2 = 2π(3)(12) + 2π(3)²
= 72π + 18π
= 90π =
V= Bh = V = πr² h  need to find r and h
V= π(r)²h = 9π(12) = 108π =

6. Example 2 8
Find the surface area and the volume of the cylinder to the right 14
SA = 2πrh + 2πr2  need to find r and h
SA = 2πrh + 2πr2 = 2π(4)(14) + 2π(4)²
= 112π + 32π
= 144π =
V= Bh = V = πr² h  need to find r and h
V= π(r)²h = 16π(14) = 224π =

7. Prisms – Areas & Volumes
Regular Triangular Prism l
Net
LA = 3 • b • l = Perimeter • l
Bases Area = 2 • ½ • b • h
SA = LA + BA
SA = 3 • b • l + b • h b h b b b
base perimeter
Surface Area (SA) – Sum of each area of (all) the faces of the solid
Lateral Area (LA) – Sum of each area of the non-base(s) faces of the solid
Surface Area = Lateral Area + Base(s) Area
Rectangular Prism
LA = 2 • w • h + 2 • L • h
Bases Area = 2 • L • w
SA = LA + BA
SA = 2(Lw + Lh + wh)
Volume (V) = B • h
Base Area (B) = L • w
V = L • w • h h w L

8. Example 1
Find the surface area and the volume of the cube to the right 8
SA = LA + BA
LA = 4· w · l = Perimeter · l and Bases Area = 2 · w h
SA = 4 · w · l + 2 w · h
h = l = w = 8
SA = 4(8)(8) + 2(8)(8) = = square units
V = B l = w h l
V = (8)(8)(8) = 512 cubic units

9. Example 2 10 4
Find the surface area and the volume of the rectangular prism to the right 6
SA = LA + BA
LA = 2(w+h) · l = Perimeter · l and Bases Area = 2 · w h
SA = 2(w · h) + 2(h · l ) + 2 (w · h)
h = 6, l = 10 and w = 4
SA = 2(4)(10) + 2(6)(10) + 2(4)(6) = = square units
V = B l = w h l
V = (4)(6)(10) = 240 cubic units

10. Example 3
Find the surface area and the volume of the isosceles triangle prism to the right c c 4 15 6
SA = LA + BA
LA = 2 · c · l + 6 · l = Perimeter · l and Bases Area = 2 · (½ b h)
SA = 2 · c · l + 6 · l + b · h
b = 6, l = and use Pythagorean theorem to find c c² = 3² + 4²
c = 5
SA = 2(5)(15) + 6(15) + (6)(4) = = square units
V = B l = ½ b h l where h is the height of the triangular base!
V = ½ (6)(4)(15) = 180 cubic units

11. Find the surface area of the cylinder.
The radius of the base and the height of the cylinder are given. Substitute these values in the formula to find the surface area.
Surface area of a cylinder
Use a calculator.
Answer: The surface area is approximately sq ft.
Example 4-2a

12. Find the volume of the cylinder to the nearest tenth.
The height h is 1.8 cm, and the radius r is 1.8 cm.
Volume of a cylinder
r 1.8, h 1.8
Use a calculator.
Answer: The volume is approximately 18.3 cubic cm.
Example 1-3a

13. Find the surface area of the triangular prism.
SA = 2B + LA
S.A. of a prism
B = ½ b h Base area = area of ∆
B = ½ (12) (8) ∆b=12, ∆h=8
B = Simplify
LA = Ph
P = c
c² = 8² + 6² = = 100
c = 10
Pythagorean Thrm
P = = 32
LA = Ph = 32 (10) = 320
SA = 2B + LA = 2 (48) = 416
Answer: 416 units2
Example 3-2c

14. Find the volume of the triangular prism.
V Bh Volume of a prism
1500 Simplify.
Answer: The volume of the prism is 1500 cubic centimeters.
Example 1-1a

15. Summary & Homework Summary: Homework:
Lateral surface area (LA) is the area of the sides
Base surface area (B) is the area of the top/bottom
Surface area = Lateral Area + Base(s) Area
Prism
Volume: V = Bh Surface Area: SA = LA + 2B
Triangular and Rectangular prisms on formula sheet
Cylinder
Volume: V= πr² h Surface Area: SA = 2πrh + 2πr² = 2πr(r+h)
Homework:
pg 692; 7-16