Post on 27-Dec-2015
Ch 12.2
A = (π)(42) = 8π 2
A = (π)(122) = 144π
Find the area of the circle.
Find the area of the sector.
Find the area of the sector.A = (π)(222)135 = 1089π 360
Ch 12.2Surface Areas of
Prisms & Cylinders
Standard 8.0Students know, derive, and solve problems
involving the area of common geometric figures.
Learning Target:I will be able to solve problems involving areas of prisms and cylinders.
Ch 10.5Ch 12.2
Theorem 12-1
Ch 12.2
Lateral Area:The sum of the areas of the lateral faces of a solid.
Lateral Faces:The faces that are not bases.In a prism, the lateral faces are parallelograms.
Lateral Area of a Prism
Find the lateral area of the regular hexagonal prism.
The bases are regular hexagons. So the perimeter of one base is 6(5) or 30 centimeters.
Answer: The lateral area is 360 square centimeters.
Lateral area of a prism
P = 30, h = 12
Multiply.
Ch 12.2
A. 162 cm2
B. 216 cm2
C. 324 cm2
D. 432 cm2
Find the lateral area of the regular octagonal prism.
Ch 12.2
Lateral area of a prism
P = 24, h = 9
Multiply.
= (3 * 8) (9)
= 216
Ch 12.2
Theorem 12-2
Surface Area:The sum of the areas of all surfaces of a solid figure.
Solid Figure:A figure that encloses a part of space.In a prism, the lateral faces are parallelograms.
Surface Area of a Prism
Find the surface area of the rectangular prism.
Ch 12.2
Surface area of a prism
P = 24, h = 12, B = 36
Simplify.
= [(6 * 4) (12)] + 2 (6 * 6)
= 360
S = L + 2B
A. 320 units2
B. 512 units2
C. 368 units2
D. 416 units2
Find the surface area of the triangular prism.
Ch 12.2
Surface area of a prism
P = 32, h=10, B = 48
Simplify.
= [(10+10+12)(10)] + 2 (½)(12*8)
= 416
S = L + 2B
Ch 12.2
Theorem 12-3 & 12-4
Lateral Area and Surface Area of a Cylinder
Find the lateral area and the surface area of the cylinder in terms of π
L = Ph Lateral area of a cylinder
= 2rh P = 2πr (circumference of a circle)
= 2(14)(18) r = 14 , h = 18.
≈ 504π Simplify.
Ch 12.2
S = L + 2B Surface area of a cylinder
= 504π + 2r2 L = 504π , B = π r2
≈ 504π + 2(14)2 r = 14
≈ 896π Simplify.
A. lateral area ≈ 480π ft2 andsurface area ≈ 768π ft2
B. lateral area ≈ 480π ft2 andsurface area ≈ 384π ft2
C. lateral area ≈ 240π ft2 andsurface area ≈ 768π ft2
D. lateral area ≈ 240π ft2 andsurface area ≈ 384π ft2
Find the lateral area and the surface area of the cylinder in terms of π.
Ch 12.2
Find Missing Dimensions
MANUFACTURING A soup can is covered with the label shown. What is the radius of the soup can?
L = Ph Lateral area of a cylinder
= 2rh P = 2π r (circumference of a circle)
125.6 = 2r(8) L = 15.7 × 8 , h = 8.
125.6 = 16r Simplify.
7.85/π = r Divide each side by 16.
Ch 12.2
A. 12 inches
B. 16 inches
C. 18 inches
D. 24 inches
Find the diameter of a base of a cylinder if the surface area is 480 square inches and the height is 8 inches.
Ch 12.2