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Algebra 1 Surface area of solid Figures

Algebra 1 Surface area of solid Figures. Warm Up. 1) Calculate the volume of the Triangular prism with altitude = 7.6 cm , base = 11 cm and the height is = 15 cm.

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Algebra 1 Surface area of solid Figures

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  1. Algebra 1Surface area of solid Figures CONFIDENTIAL

  2. Warm Up 1) Calculate the volume of the Triangular prism with altitude = 7.6 cm , base = 11 cm and the height is = 15 cm. 2) The given cylinder has radius = 13 cm and the height = 16 cm. A cone of radius = 9 cm and height = 13 cm is cut from the cylinder. What is the volume of the remaining piece? 3) If the volumes of two cubes are in the ratio 64 : 1, then what is the ratio of their edges? 4) The radius of a cylinder is decreased to 1/5th of the original radius. How many times will its height increase, if its volume remains the same? CONFIDENTIAL

  3. Surface area The surface area of a solid figure is the sum of the areas of all faces of the figure. An area of study closely related to solid geometry is nets of a solid. Imagine making cuts along some edges of a solid and opening it up to form a plane figure. The plane figure is called the net of the solid. The surface area of a rectangular solid is expressed in square units. CONFIDENTIAL

  4. In general, Surface Area of solid figures = 2 x area of the base +perimeter of the base x height If, B = area of the base P = perimeter of the base h = height SA = Surface Area Then, SA = 2B +Ph CONFIDENTIAL

  5. s s s s s s s s s Cubes A cube is a three-dimensional figure with all edges of the same length. If s is the length of one of its sides, then SA = 2(s2) + (4s)s = 6s2 CONFIDENTIAL

  6. 7 7 7 Calculate the surface area of the cubewith length of sides = 7 cm. Volume of the cube = 6s2 = 6 x (7)2 = 6 x 49 = 294 Surface Area of the cube = 294cm2 CONFIDENTIAL

  7. c d a b c d b h h b a Triangular prism SA = 2( 1 ) + (b + c + d)h 2ab SA = ab + (b + c + d)h CONFIDENTIAL

  8. 5 8 10 Calculate the surface area of the regular triangular prism. Surface area of the triangular prism = a x b + (b + c + d)h = 5 x 8 + (8 + 8 + 8) x 10 = 40 + 240 = 280 Surface areaof the cuboid= 280cm2 CONFIDENTIAL

  9. 5 8 6 11 8 7 Now you try! 1) The surface area of a cube is 294 ft2. Find the length of each edge. 2) Calculate the surface area of the given triangular prism. CONFIDENTIAL

  10. h w l h w l Rectangular prism SA = 2B + Ph SA = 2(lw) + (2l + 2w)h CONFIDENTIAL

  11. 7 4 8 Calculate the surface area of the given rectangular prism. Surface area of the rectangular prism = 2(lw) + (2l + 2w)h = 2(8 x 4) + (2 x 8 + 2 x 4)x 7 = 2 x 32 + (16 + 8)x 7 = 64 + 168 = 232 Surface areaof the rectangular prism= 268cm2 CONFIDENTIAL

  12. h s s h s Regular square prism SA = 2B + Ph SA = 2(s2) + (4s)h CONFIDENTIAL

  13. 11 8 8 Calculate the surface area of the given Regular square prism. Surface area of the Regular square prism = 2(s2) + (4s)h = 2(8 x 8) + (4 x 8)x 11 = 2 x 64 + 32x 11 = 128 + 352 = 480 Surface area of the regular square prism= 480cm2 CONFIDENTIAL

  14. h a h s a s Regular pentagonal prism SA = 2(1ans) + nsh 2 SA = 2(1a)(5)s + 5sh 2 SA = 5as + 5sh CONFIDENTIAL

  15. 9 6 8 Calculate the surface area of the given Regular pentagonal prism. Surface area of the Regular square prism = 5as + 5sh = 2 x 6 x 8 + 5 x 8 x 9 = 2 x 48 + 5x 72 = 96 + 360 = 456 Surface areaof the regular square prism= 456 cm2 CONFIDENTIAL

  16. 6 3 4 Now you try! 1) The surface area of a regular square prism is 294 ft2 and height 10 ft. Find the length of each edge of the base. 2) Calculate the surface area of the given Regular pentagonal prism. CONFIDENTIAL

  17. l s a s a l Regular triangular pyramid SA = B + n(1sl) 2 SA = 1as + (3)(1sl) 2 2 SA = 1as + 3sl 2 2 l = slant height CONFIDENTIAL

  18. 5 6 4 Calculate the surface area of the given Regular triangular pyramid. Surface area of the Regular triangular pyramid = 1as + 3sl 2 2 = 1 x 4 x 6 + 3 x 6 x 5 2 2 = 18 + 45 = 63 Surface areaof the regular triangular pyramid= 63 cm2 CONFIDENTIAL

  19. l h s s s l Regular square pyramid SA = B + n(1sl) 2 SA = s2 + (4)(1sl) 2 SA = s2 + 2sl CONFIDENTIAL

  20. 7 h 8 8 Calculate the surface area of the given Regular square pyramid. Surface area of the Regular square pyramid = s2 + 2sl =8 x 8 + 2 x 8 x 7 = 64 + 112 = 176 Surface areaof the regular squarepyramid= 176 cm2 CONFIDENTIAL

  21. 5 9 h 9 8 10 10 Now you try! 1) Calculate the surface area of the given Regular triangular pyramid. 2) Calculate the surface area of the given Regular square pyramid. CONFIDENTIAL

  22. P r h h r Cylinder SA = 2B + Ph SA = 2(Π r2) + (2 Πr)h CONFIDENTIAL

  23. 5 8 Calculate the surface area of the given cylinder. Surface area of the cylinder = 2(Π r2) + (2 Πr)h =2 x (3.14 x 5 x 5 ) + (2 x 3.14 x 5 ) x 8 = 157 + 251.2 = 408.2 Surface areaof the cylinder= 408.2 cm2 CONFIDENTIAL

  24. r Sphere SA = 4 Πr2 CONFIDENTIAL

  25. 10 Calculate the surface area of the given sphere. Surface area of the sphere = 4 Πr2 =4 x 3.14 x 10 x 10 = 1256 Surface areaof the sphere= 1256 cm2 CONFIDENTIAL

  26. 7 10 8 Now you try! 1) Calculate the surface area of the given cylinder. 2) Calculate the surface area of the given sphere. CONFIDENTIAL

  27. Assessment 1) What is the perimeter of the floor, if the area of the four walls is equal to 2700 ft2 and its height is 12 ft? 2) The perimeter of one face of a cube is 48 cm. What is its surface area? CONFIDENTIAL

  28. 8 9 7 3) The base radius of a cylinder is 2 cm and its height is 5 cm. What is the resultant surface area of the cylinder, if the radius is increased by 2 times? 4) Calculate the surface area of the given Regular triangular pyramid. CONFIDENTIAL

  29. 6 h 7 7 7 3 4.5 5) Calculate the surface area of the given Regular pentagonal prism. 6) Calculate the surface area of the given Regular square pyramid. CONFIDENTIAL

  30. 6) Calculate the surface area of the spherewith radius = 34 cm. 7) The base area of a square pyramidis 49 in2. What is the surface area of the pyramid, if the slant height of the pyramidis 12 in? CONFIDENTIAL

  31. 8) A rectangular tin sheet of 44 in. long and 20 in. broad is rolled along its length to form a cylinder by making the opposite edges just touch each other. What is the base radius of the cylinder formed? 9) What is the lateral area of a cube, if the area of each face of the cube is 16 ft2? CONFIDENTIAL

  32. 3 10 5 7 10 10) The figure shows a rectangular prism with a cylinder which has been removed from it. What is the total surface area of the given solid? Round the answer to the nearest ten. CONFIDENTIAL

  33. Let’s review In general, Surface Area of solid figures = 2 x area of the base +perimeter of the base x height If, B = area of the base P = perimeter of the base h = height SA = Surface Area Then, SA = 2B +Ph CONFIDENTIAL

  34. s s s s s s s s s review Cubes A cube is a three-dimensional figure with all edges of the same length. If s is the length of one of its sides, then SA = 2(s2) + (4s)s = 6s2 CONFIDENTIAL

  35. c d a b c d b h h b a review Triangular prism SA = 2( 1 ) + (b + c + d)h 2ab SA = ab + (b + c + d)h CONFIDENTIAL

  36. h w l h w l review Rectangular prism SA = 2B + Ph SA = 2(lw) + (2l + 2w)h CONFIDENTIAL

  37. h a h s a s review Regular pentagonal prism SA = 2(1ans) + nsh 2 SA = 2(1a)(5)s + 5sh 2 SA = 5as + 5sh CONFIDENTIAL

  38. l s a s a l review Regular triangular pyramid SA = B + n(1sl) 2 SA = 1as + (3)(1sl) 2 2 SA = 1as + 3sl 2 2 l = slant height CONFIDENTIAL

  39. l h s s s l review Regular square pyramid SA = B + n(1sl) 2 SA = s2 + (4)(1sl) 2 SA = s2 + 2sl CONFIDENTIAL

  40. P r h h r review Cylinder SA = 2B + Ph SA = 2(Π r2) + (2 Πr)h CONFIDENTIAL

  41. r review Sphere SA = 4 Πr2 CONFIDENTIAL

  42. You did a great job today! CONFIDENTIAL

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