Unit 30 SPHERES AND COMPOSITE FIGURES VOLUMES SURFACE

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

SPHERES o o 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 2

SPHERES The surface area of a sphere equals 4 r 2 where r is the radius The volume of a sphere equals 4/3 r 3 where r is the radius 3

SPHERE EXAMPLE o Determine the surface area and volume of a basketball that has a 12 -cm radius: SA = 4 r 2 = 4 (12 cm)2 = 1809. 56 cm 2 Ans V = 4/3 r 3 = 4/3 (12 cm)3 = 7238. 23 cm 3 Ans 4

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

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

COMPOSITE FIGURE EXAMPLE (Cont) o 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 in 2 4" 30" 6" – Area of triangle = ½(10")(6") = 30 in 2 – Area of circle = (2")2 = 12. 57 in 2 10" 45" – Total surface area of composite figure: = 1350 in 2 – 30 in 2 – 12. 57 in 2 = 1307. 43 in 2 Ans 7

PRACTICE PROBLEMS o Round all answers to the following problems to two decimal places whenever necessary: 1. 2. 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. 8

PRACTICE PROBLEMS (Cont) o Round all answers to the following problems to two decimal places whenever necessary: 3. 4. 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. 9

PRACTICE PROBLEMS (Cont) 5. Determine the volume of the bullet shown below: 10

PROBLEM ANSWER KEY 1. 2. 3. 4. 5. SA = 2463. 01 mm 2 V = 11494. 04 mm 3 $56. 30 2010. 62 gallons 198. 95 in 2 11434. 35 cm 3 11