Math Workshop II

Unit 4

Surface Area

Name ___________________ Pd ________

4-11 Surface Area of Cylinders Surface Area - _____________________________________________________________________________ Units – Cylinder: h

r

Formula: SA= 2πrh + 2πr2 r = radius of the base h = height Ex. 1: Find the surface area of a cylinder with top radius 2 m and height of 6 m. Ex. 2: Find the surface area of a cylinder with top diameter 6 in. and length 20 in. PSSA Practice: Before wooden telephone poles are installed, they are treated with creosote. If creosote costs $.50 per square foot, how much does it cost to treat a pole that is 12 ft. tall and 1 foot wide?

4-11 Classwork Cylinders Find the surface area of a cylinder with the given dimensions. Round to the nearest tenth. SA = 2π r2 + 2π rh

1. r = 6 in, h = 12 in 2. r = 8 cm, h = 10 cm

3. d = 2.5 ft, h = 19 ft 4. d = 12 yd, h = 15 yd

Find the surface area of each cylinder shown.

5. 6. 3 ft

9.5 m

7.5 m 8 ft Find the height of each cylinder:

7. Surface area is 226.2 square centimeters, radius is 2 meters.

8. Surface area is 1520.5 square yards, radius is 5 yards.

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4-11 Cylinders Find the surface area of a cylinder with the given dimensions. Round to the nearest tenth. SA = 2π r2 + 2π rh

1. r = 5 in, h = 14 in 2. r = 10 cm, h = 15 cm

3. r = 4 ft, h = 26 ft 4. d = 18 yd, h = 4 yd

5. d = 8 m, h = 9 m 6. d = 22 mm, h = 22 mm

Find the surface area of each cylinder shown.

7. 8. 4 ft

8.5 m

5 m 7 ft Find the height of each cylinder:

9. Surface area is 603.2 square meters, radius is 3 meters

10. Surface area is 100.5 square inches, radius is 4 inches

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4-12 Surface Area of a Cone Formula for the Surface Area of a Cone: SA = π r l +π r2

r = radius of base l = slant height

r

h = the height of the cone h

l

Ex. 1: Find the surface area of a cone with base radius 6 in. and slant height 15 in. Ex. 2: Find the surface area of a cone with base radius 3 m. and height 4 m. Ex. 3: Find the surface area of a cone with height 12 ft. and slant height 13 ft.

4-12 Surface Area of a Cone PSSA Example: If the top of a silo is made out of sheet metal in the shape of a cone, how much would the silo lid cost if sheet metal cost $2.00 per square foot and the cone will need to 10 feet high and have a base radius of 30 feet? Explain your answer.

4-12 Classwork CONES Find the surface area of each cone. Round to the nearest tenth. SA = πr l + πr2

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4-12 CONES Find the surface area of each cone. Round to the nearest tenth. SA = πr l + πr2

l2 = 52 + 142 l2 = 252 + 102

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r2 = 152 - 122

r2 = 122 - 92

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4-13 Surface Area of Prisms Formula for the Surface Area of a Prism: SA = 2B + Ph B = area of the base P = perimeter of the base h = height of the prism

Lateral Face (4)

Base (2) h Ex. 1: Find the surface area of a rectangular prism with height 6 in., width 5 in. and length 10 in. PSSA Practice: How much wrapping paper is necessary to wrap a box whose dimensions are 6 in. x 4 in. x 8 in.? In words, explain how you found your solution.

4-13 Classwork Prism Find the lateral area of each prism. LA. = Ph

9.4

Find the surface area of each prism. Round answers to nearest tenth. SA = 2B + Ph

10.3

14.3

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4-13 Prism Find the lateral area of each prism. LA. = Ph

Find the surface area of each prism. Round answers to nearest tenth. SA = 2B + Ph

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4-14 Surface Area of Pyramids Formula: SA = ½ P l + B

l

P =perimeter of base l = slant height – height of one triangle face

B = area of base Ex. 1: Find the SA of a pyramid with a base of 8 m and slant height of 9 m. PSSA Example: How much would it cost to paint a Pyramid whose slant height is 150 feet and whose base is 200 feet if paint costs $.75 per square foot? In words, explain how you found your solution.

4-14 Classwork Pyramid Find the surface area of each pyramid. Round to the nearest tenth. SA = ½ P l + B

Base = 21.2 m2

Base = 43 ft2 Base= 26.2 cm2

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Base = 586.9 mm2

side = 13.1 mm

l = 12.2 m

Base = 23.4 yd2

l = 9.8 yd

9. The roof of a gazebo is a regular octagonal pyramid. If the base of the pyramid has sides of .5 meters and the slant height of the roof is 1.9 meters, find the area of the roof.

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4-14 Pyramid Find the surface area of each pyramid. Round to the nearest tenth. SA = ½ P l + B

Base = 166.3 in2

L = 13.9 Base = 142.8 m2

l = 12.5

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Base = 15.6 mm2

l = 10.4

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4-15 Surface Area of a Sphere Formula for the Surface Area of a Sphere: SA = 4 π r2

Radius DC , DA , DB

Chord FG , AB

Diameter AB

Tangent JH Great circle is formed when a plane intersects a sphere through a diameter (center of the sphere)

The great circle divides the sphere into 2 hemispheres Ex. 1: Find the surface area of a sphere with a radius of the great circle 5 inches.

4-15 Surface Area of a Sphere Ex. 2: Find the surface area of a sphere with the diameter of the great circle 16 m. PSSA Practice: If leather costs $3.00 per square foot, how much does it costs to wrap a basketball of radius 1 ft. in leather? In words, explain how you found your solution.

4-15 Classwork SPHERES In the figure, A is the center of the sphere, and plane T intersects the sphere in circle E. Round to the nearest tenth if necessary.

1. If AE = 5 and DE = 12, find AD. a2 + b2 = c2

2. If the radius (AD) of the sphere is 18 units and the radius (ED) of circle E is 17 units, find AE. a2 + b2 = c2

Find the surface area of each sphere or hemisphere. Round to the nearest tenth. SA = 4π r2

3. A hemisphere with a radius of the great circle 8 yards. 4. A hemisphere with a radius of the great circle 2.5 millimeters.

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5. A sphere with the area of a great circle 28.6 inches.

8. Find the surface area of a sphere with a radius of 8 ft.

9. Find the surface area of a sphere with a diameter of 24 cm.

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4-15 SPHERES

Find the surface area of each sphere given the radius or diameter of the sphere. 11. r = 8 cm 12. r = 2.3 ft 13. r = π in 14. d = 10 in 15. d = 16 yd 16. d = 8.4 cm

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17. Find the surface area of a hemisphere with a radius of 12 cm. 18. Find the surface area of a hemisphere with a diameter of 4π .

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REVIEW WORKSHEET FOR SURFACE AREA NAME___________________________

Name each of the figures A-L.

1. _________________________ 2. _________________________ 3. _________________________ 4. _________________________ 5. _________________________ 6. _________________________ 7. _________________________ 8. _________________________

9. _________________________ 10. _________________________ 11. _________________________ 12. _________________________

For each formula for surface area, identify what each letter represents.

13. rectangular prism SA= 2wh + 2wl + 2lh l = _________ w = __________ h = ___________

14. cylinder SA= 2π rh + 2π r2 r = _________ h = ___________

15. cone SA= π r2 + π r 22 hr + r = __________ h= ___________

or SA=π r2 + π r l l = _________

16. pyramid SA= ½ Pl + B P = ___________ l = _________ B = _______________

17. sphere SA= π d2 or 4π r2 r = ___________ d = ____________

18. what is the value of π ? ________________ - 17 -

Find the total surface area for each of the following figures.

19. 20. 21. 22. 23. 24.

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6 in.

4 ft

25. How many square inches of cardboard are needed to build a box that has of length

7 inches, a width of 10 inches, and a height of 8 inches? (show all work)

26. Use the drawing of the water tank to answer the following questions. (show all work)

a) What three separate geometric figures are used

to make the water tank in the drawing ?

b) What is the overall height of the tank?

c) How much metal would it take to make the top part of the tank?

d) How much metal would it take to make the middle part of the tank?

e) How much metal would it take to make the bottom part of the tank?

f) How much metal would it take to make the entire tank?

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