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  r 2 where r is the radius The volume of a sphere equals 4/3  r 3 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  r 2 = 4  (12 cm) 2 = cm 2 Ans V = 4/3  r 3 = 4/3  (12 cm) 3 = cm 3 Ans

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

7 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 10" 45" 30" 6" 4" –Area of rectangle = 30"  45" = 1350 in 2 –Area of triangle = ½(10")(6") = 30 in 2 –Area of circle =  (2") 2 = in 2 –Total surface area of composite figure: = 1350 in 2 – 30 in 2 – in 2 = in 2 Ans

8 PRACTICE PROBLEMS  Round all answers to the following problems to two decimal places whenever necessary: 1. Determine the surface area and volume of a sphere with a radius of 14 mm. 2. 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: 3. How many gallons of water will the tank in problem #2 hold? 4. Compute the surface area of a ball that has a circumference (great circle) of 25 inches.

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

11 PROBLEM ANSWER KEY 1. SA = mm 2 V = mm 3 2. $ gallons in cm 3