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Please start Bellwork # HW, red pen, book on desk.

Please start Bellwork # HW, red pen, book on desk. 3-23-11. HW, red pen, book on desk. Surface Area: Prisms and Cylinders. Lesson 10-5 p.527. Surface Area. Surface area is the area of the sum of all of the surfaces of a space figure. In other words, it is the area of the net.

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Please start Bellwork # HW, red pen, book on desk.

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  1. Please start Bellwork # • HW, red pen, book on desk.

  2. 3-23-11 • HW, red pen, book on desk.

  3. Surface Area: Prisms and Cylinders Lesson 10-5 p.527

  4. Surface Area • Surface area is the area of the sum of all of the surfaces of a space figure. • In other words, it is the area of the net.

  5. Surface Area 3 cm 2 cm 5 cm 3 cm Notice that there are 2 bases (front and back) that are identical. There are also two faces (the top and bottom) that are identical. In addition there are two sides (right and left) that are identical.

  6. Surface Area • To find the surface area, find the area of each surface and add them together. First, let’s calculate the front and back: A = bh A = 3 (2) = 6 sq. cm. for the front and 6 sq. cm. for the back. Next, let’s look at the top and bottom: A = bh A = 5 (3) = 15 sq. cm for the top and 15 sq. cm for the bottom. Last, let’s calculate the right and left sides A = bh A = 5 (2) = 10 sq. cm for the right side and 10 sq. cm for the left side. 3 cm 2 cm 5 cm 3 cm

  7. Surface Area • To find the surface area, find the area of each surface and add them together. First, let’s calculate the front and back: A = bh A = 3 (2) = 6 sq. cm. for the front and 6 sq. cm. for the back. Next, let’s look at the top and bottom: A = bh A = 5 (3) = 15 sq. cm for the top and 15 sq. cm for the bottom. Last, let’s calculate the right and left sides A = bh A = 5 (2) = 10 sq. cm for the right side and 10 sq. cm for the left side. 3 cm 2 cm 5 cm 3 cm If we add up all the areas, (6 + 6 + 15 + 15 + 10 + 10) we get 62 sq. cm. That is the total surface area of the prism.

  8. Surface Area • Another way to calculate the surface area is to measure the net: 3 cm 5 cm 2 cm 5 cm 2 cm 3 cm 3 cm

  9. Surface Area • Another way to calculate the surface area is to measure the net: 6 3 cm 5 cm 10 15 10 2 cm 5 cm 6 2 cm 3 cm 3 cm If you calculate the area of each face (or piece) the answer is still 62 sq. cm. 15

  10. Try This • Find the surface area: 3 in 10 in 4 in

  11. Try This • Find the surface area: 164 sq. in. 3 in 10 in 4 in

  12. Surface Area • We can do the same procedure with a triangular prism: How many faces or surfaces are there? 6 ft 5 ft 3 ft 4 ft

  13. Surface Area • We can do the same procedure with a triangular prism: How many faces or surfaces are there? Notice there are 5 surfaces. There are 2 triangles, there is the back, the floor or bottom, and the slanted face. 6 ft 5 ft 3 ft 4 ft

  14. Surface Area • First calculate the triangles: A = bh 3 (4) = 6 sq. ft. (1st triangle) 2 2 6 sq. ft. (2nd triangle) 6 ft 5 ft 3 ft 4 ft

  15. Surface Area • First calculate the triangles: A = bh 3 (4) = 6 sq. ft. (1st triangle) 2 2 6 sq. ft. (2nd triangle) Next calculate the back: A = bh A = 6 (3) = 18 sq. ft. (back) Next is the floor: A = bh A = 6 (4) = 24 sq. ft. (floor) 6 ft 5 ft 3 ft 4 ft

  16. Surface Area • First calculate the triangles: A = bh 3 (4) = 6 sq. ft. (1st triangle) 2 2 6 sq. ft. (2nd triangle) Next calculate the back: A = bh A = 6 (3) = 18 sq. ft. (back) Next is the floor: A = bh A = 6 (4) = 24 sq. ft. (floor) Add them all up for a total of 84 sq. ft. 6 ft 5 ft 3 ft 4 ft

  17. Surface Area • First calculate the triangles: A = bh 3 (4) = 6 sq. ft. (1st triangle) 2 2 6 sq. ft. (2nd triangle) Next calculate the back: A = bh A = 6 (3) = 18 sq. ft. (back) Next is the floor: A = bh A = 6 (4) = 24 sq. ft. (floor) Finally find the area of the slant: A = bh = 6 (5) = 30 sq. ft. Add them all up for a total of 84 sq. ft. 6 ft 5 ft 3 ft 4 ft

  18. Surface Area • We can also calculate the area of a cylinder. 3 m What are the shapes that make up a cylinder? 5 m

  19. Surface Area • We can also calculate the area of a cylinder. 3 m What are the shapes that make up a cylinder? Did you remember that there are two circles, and a rectangle? 5 m

  20. Surface Area • This one is best calculated by looking at the net. It is easy to calculate the area of the circles, 3 m = 3.14 (3)2 = 28.26 sq. m (remember there are 2 circles so multiply 28.26 times 2 to get 56.52 sq. m 5 cm

  21. Surface Area • So we know the circles have a total of 56.52 sq. m. but what about the rectangle? We can easily see that the height Is 5 cm, but what is the value of the base? 3 m 5 cm

  22. Surface Area • So we know the circles have a total of 56.52 sq. m. but what about the rectangle? We can easily see that the height Is 5 cm, but what is the value of the base? The base of the rectangle is the CIRCUMFERENCE of the circle. 3 m 5 cm

  23. Surface Area To find the circumference of the circle, remember the formula is So, C = 3.14 (6) = 18.84 cm 3 m 5 cm

  24. Surface Area To find the circumference of the circle, remember the formula is So, C = 3.14 (6) = 18.84 cm OK, so A = bh A = 18.84 (5) = 94.2 sq. cm. Remember that the area of the Two circles totaled 56.52 sq. cm? The last step is to add the 94.2 Plus the 56.52 to get a total of 150.72 3 m 5 cm 18.84 cm

  25. Try This • Find the surface area 4 ft. 10 ft

  26. Try This • Find the surface area 4 ft. First find the area of the two circles. What is the total of The two circles? 10 ft

  27. Try This • Find the surface area 4 ft. First find the area of the two circles. What is the total of The two circles? 10 ft 100.48 sq. ft.

  28. Try This • Find the surface area 100.48 sq. ft. (area of the two circles) 4 ft. Next find the area of the rectangle. The base is the same as the circumference of the circle. Find the circumference of the circle. 10 ft 25.12 cm

  29. Try This • Find the surface area 100.48 sq. ft. (area of the two circles) 4 ft. 25.12 cm = the base of the rectangle. Find the area of the rectangle: 10 ft

  30. Try This • Find the surface area 100.48 sq. ft. (area of the two circles) 4 ft. 25.12 cm = the base of the rectangle. Find the area of the rectangle: 10 ft A of rectangle = 251.2 sq ft.

  31. Try This • Find the surface area 100.48 sq. ft. (area of the two circles) 4 ft. A of rectangle = 251.2 sq ft. 10 ft Now find the total surface area.

  32. Try This • Find the surface area 100.48 sq. ft. (area of the two circles) 4 ft. A of rectangle = 251.2 sq ft. 10 ft Now find the total surface area. 351.68 sq. ft.

  33. PA#42 P.530 #1-6 Print out CAT 6 Review for 7th grade standards.

  34. 3-23-11 PA#43 P.530 #8-13 Print out CAT 6 Review for 7th grade standards. Pages 9-30

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