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Unit 30

Unit 30. SPHERES AND COMPOSITE FIGURES: VOLUMES, SURFACE AREAS, AND WEIGHTS. SPHERES. A sphere is a solid figure bounded by a curved surface such that every point on the surface is the same distance from a point called the center

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Unit 30

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  1. Unit 30 SPHERES AND COMPOSITE FIGURES: VOLUMES, SURFACE AREAS, AND WEIGHTS

  2. SPHERES • A sphere is a solid figure bounded by a curved surface such that every point on the surface is the same distance from a point called the center • A round ball, such as a baseball or basketball, is an example of a sphere

  3. SPHERES The surface area of a sphere equals 4r2 where r is the radius The volume of a sphere equals 4/3 r3 where r is the radius

  4. SPHERE EXAMPLE • Determine the surface area and volume of a basketball that has a 12-cm radius: SA = 4r2 = 4(12 cm)2 = 1809.56 cm2Ans V = 4/3 r3 = 4/3 (12 cm)3 = 7238.23 cm3Ans

  5. VOLUMES AND SURFACE AREAS OF COMPOSITE SOLID FIGURES • To compute volumes of composite solid figures • Determine the volume of each simple solid figure separately • Then add or subtract the individual volumes • To compute the surface areas of composite solid figures • Determine the surface area of each simple solid figure separately • Then add or subtract the individual surface areas

  6. 4" 30" 6" 10" 45" COMPOSITE FIGURE EXAMPLE • Determine the total surface area of the figure below, given that the circle and triangle are holes that were cut out • First determine the area of the rectangle • Then subtract the areas of the circle and triangle

  7. 4" 30" 6" 10" 45" COMPOSITE FIGURE EXAMPLE (Cont) • Determine the total surface area of the figure below, given that the circle and triangle are holes that were cut out • Area of rectangle = 30"  45" = 1350 in2 • Area of triangle = ½(10")(6") = 30 in2 • Area of circle = (2")2 = 12.57 in2 • Total surface area of composite figure: = 1350 in2 – 30 in2 – 12.57 in2 = 1307.43 in2Ans

  8. PRACTICE PROBLEMS • Round all answers to the following problems to two decimal places whenever necessary: • Determine the surface area and volume of a sphere with a radius of 14 mm. • A spherical water tank has a diameter of 8 feet. It is to be repainted, and the total cost of the paint job is $0.28 per square foot. Compute the total cost of repainting the tank.

  9. PRACTICE PROBLEMS (Cont) • Round all answers to the following problems to two decimal places whenever necessary: • How many gallons of water will the tank in problem #2 hold? • Compute the surface area of a ball that has a circumference (great circle) of 25 inches.

  10. PRACTICE PROBLEMS (Cont) • Determine the volume of the bullet shown below:

  11. PROBLEM ANSWER KEY • SA = 2463.01 mm2 V = 11494.04 mm3 • $56.30 • 2010.62 gallons • 198.95 in2 • 11434.35 cm3

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