Title: SPHERES AND COMPOSITE FIGURES: VOLUMES, SURFACE AREAS, AND WEIGHTS
1 UNIT 30
SPHERES AND COMPOSITE FIGURES VOLUMES SURFACE AREAS AND WEIGHTS
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
The surface area of a sphere equals 4r2 where r is the radius
The volume of a sphere equals 4/3 r3 where r is the radius
3 SPHERE EXAMPLE
Determine the surface area and volume of a basketball that has a 12-cm radius
SA 4r2 4(12 cm)2 1809.56 cm2 Ans
V 4/3 r3 4/3 (12 cm)3 7238.23 cm3 Ans
4 VOLUMES AND SURFACE AREAS OF COMPOSITE SOLID FIGURES
To compute volumes and surface areas of composite solid figures it is necessary to determine the volume or surface area of each simple solid figure separately. The individual volumes or areas are then added or subtracted
5 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 and then subtract the areas of the circle and triangle
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 in2 Ans
6 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.
3. How many gallons of water will the tank in problem 2 hold given that 7.5 gallons 1 cubic foot
4. Compute the surface area of a ball that has a circumference (great circle) of 25 inches.
7 PRACTICE PROBLEMS
5. Determine the volume of the figure shown below
8 PROBLEM ANSWER KEY
1. SA 2463.01 mm2
V 11494.04 mm3
3. 2010.62 gallons
4. 198.95 in2
5. 11434.35 cm3
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