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Formulas and examples for calculating the surface area and volume of spheres. It explains the concepts of radius, diameter, chord, and great circles, and demonstrates how to find the surface area and volume using these measurements. three examples with solutions.
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Typology: Lecture notes
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A circle is described as a locus of points in a plane that are a given distance from a point. A sphere is the locus of points in space that are a given distance from a point.
Surface Area of a Sphere
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2 The surface area of the sphere in part (b) is four times greater than the surface area of the sphere in part (a) because 16 • 4 = 64 So, when the radius of a sphere doubles, the surface area DOES NOT double.
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Solution: Begin by finding the radius of the sphere. C = 2r 13.8 = 2r 13.8 2 r 6.9 = r = r
Solution: Using a radius of 6.9 feet, the surface area is: S = 4r 2 = 4(6.9) 2 = 190.44 ft. 2
Ex. 3: Finding the Surface Area of a Sphere
More... V n(1/3)Br = 1/3 (nB)r 1/3(4r 2 )r =4/3r 2 Each pyramid has a volume of 1/3Br. Regroup factors. Substitute 4r 2 for nB. Simplify.
Volume of a Sphere
Solution:
More... V =4/3r 3 2 = 4/3r 3 6 = 4r 3 1.5 = r 3 1.14 r Formula for volume of a sphere. Substitute 2 for V. Multiply each side by 3. Divide each side by 4. Use a calculator to take the cube root. So, the radius of the ball bearing is about 1.14 cm.