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MATH 3190

MATH 3190. Surface Area and Volume. 7 cm. 5 cm. 6 cm. Measurement. Rectangular Prism Surface Area : sum of the areas of all of the faces

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MATH 3190

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  1. MATH 3190 Surface Area and Volume

  2. 7 cm 5 cm 6 cm Measurement • Rectangular Prism • Surface Area: sum of the areas of all of the faces • Example: There are 4 lateral faces: 2 lateral faces are 6 cm by 7 cm (A1= wh) and 2 lateral faces are 5 cm by 7 cm (A2 = lh). There are 2 bases 6 cm by 5 cm (A3 = lw) • A1 = (6 cm)(7 cm) = 42 cm2 • A2 = (5 cm)(7 cm) = 35 cm2 • A3 = (6 cm)(5 cm) = 30 cm2 • SA rectangular prism = 2wh + 2lh + 2lw • SA = 2(42 cm2) + 2(35 cm2) + 2(30 cm2) • SA = 84 cm2 + 70 cm2 + 60 cm2 • SA = 214 cm2

  3. 5 cm Measurement • Cube • Surface Area: sum of the areas of all 6 congruent faces • Example: There are 6 faces: 5 cm by 5 cm (A = s2) • SA cube = 6A = 6s2 • SA = 6(5 cm)2 • SA = 6(25 cm2) • SA = 150 cm2

  4. 7 m 5 m 6 m Measurement • Triangular Prism • Surface Area: sum of the areas of all of the faces • Example: There are 3 lateral faces: 6 m by 7 m (A1= bl). There are 2 bases: 6 m for the base and 5 m for the height (2A2 = bh). • A1 = (6 m)(7 m) = 42 m2 • 2A2 = (6 m)(5 m) = 30 m2 • SA triangular prism = bh + 3bl • SA = 30 m2 + 3(42 m2) • SA = 30 m2 + 126 m2 • SA = 156 m2

  5. 3 ft 12 ft Measurement • Cylinder • Surface Area: area of the circles plus the area of the lateral face • Example: r = 3 ft; h = 12 ft • SA cylinder= 2rh +2r2 • SA = 2 (3 ft)(12 ft) + 2 (3 ft)2 • SA = 72 ft2 + 2 (9 ft2) • SA = 72 ft2 + 18 ft2 • SA = 90 ft2

  6. 13 ft 12 ft 5 ft Measurement • Cone • Surface Area: area of the circle plus the area of the lateral face • Example: r = 5 ft; t = 13 ft • SA cone= rt +r2 • SA = (5 ft)(13 ft) +  (5 ft)2 • SA = 65 ft2 +  (25 ft2) • SA = 65 ft2 + 25 ft2 • SA = 90 ft2

  7. 8 mm Measurement • Sphere • Surface Area: 4r2 where r is the radius • Example: r = 8 mm • SA sphere = 4r2 • SA = 4(8 mm)2 • SA = 4(64 mm2) • SA = 256 mm2

  8. 7 cm 5 cm 6 cm Measurement • Rectangular Prism • Volume: • V = lwh where l is length; w is width; and h is height • Example: l = 6 cm; w = 5 cm; h = 7 cm • V rectangular prism = Bh = lwh • V = (6 cm)(5 cm)(7 cm) • V = 210 cm3

  9. 5 cm Measurement • Cube • Volume: • V = s3 where s is the length of a side • Example: s = 5 cm • V cube = Bh = s3 • V = (5 cm)3 • V = 125 cm3

  10. 7 m 5 m 6 m Measurement • Triangular Prism • Volume: • V = ½ bhl where b is the base; h is height of the triangle; and l is length of the prism • Example: b = 6 m; h = 5 m; l = 7 m • V triangular prism = Bh = ½ bhl • V = ½ (6 m)(5 m)(7 m) • V = 105 m3

  11. 3 ft 12 ft Measurement • Cylinder • Volume of a Cylinder: V = r2h where r is the radius of the base (circle) and h is the height. • Example: r = 3 ft and h = 12 ft. • V cylinder = Bh = r2h • V = (3 ft)2 (12 ft) • V = (9 ft2)(12 ft) • V = 108 ft3

  12. 13 ft 12 ft 5 ft Measurement • Cone • Volume: V = r2h/3 where r is the radius of the base (circle) and h is the height. • Example: r = 5 ft; h = 12 ft • V cone= r2h/3 • V = [(5 ft)2 12 ft ]/ 3 • V = [(25 ft2)(12 ft)]/3 • V = (25 ft2)(4 ft) • V = 100 ft3

  13. 6 mm Measurement • Sphere • Volume of a Sphere: V = (4/3) r3 where r is the radius • Example: r = 6 mm • V sphere = 4r3/3 • V = [4 x (6 mm)3]/3 • V = [4 x 216 mm3]/3 • V = [864 mm3]/3 • V = 288 mm3

  14. Measurement • Triangular Pyramid • Square Pyramid

  15. Test Taking Tips • Get a good nights rest before the exam • Prepare materials for exam in advance (scratch paper, pencil, and calculator) • Read questions carefully and ask if you have a question DURING the exam • Remember: If you are prepared, you need not fear

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