Volumes of Spheres and Other Solid Figures Adapted from Walch Education.

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Presentation transcript:

Volumes of Spheres and Other Solid Figures Adapted from Walch Education

Sphere A sphere is a three-dimensional surface that has all its points the same distance from its center. The formula for the volume of a sphere is 3.5.3: Volumes of Spheres and Other Solid Figures 2

Practice A teenager buying some chewing gum is comparing packages of gum in order to get the most gum possible. Each package costs the same amount. Package 1 has 20 pieces of gum shaped like spheres. Each piece has a radius of 5 mm. Package 2 has 5 pieces of gum shaped like spheres. Each piece has a radius of 10 mm. Which package should the teenager buy? Round to the nearest millimeter : Volumes of Spheres and Other Solid Figures 3

Step 1 Find the volume of a piece of gum in package 1 by using the volume formula for a sphere : Volumes of Spheres and Other Solid Figures 4 Formula for volume of a sphere Substitute 5 for r.

Step 2 Multiply the volume of the single piece of gum in package 1 by 20 to get the total volume of the gum in the package. (524)(20) = 10,480 mm : Volumes of Spheres and Other Solid Figures 5

Step 3 The radius of each piece of gum in package 2 is 10 mm. Find the volume of a piece of gum in package 2 by using the volume formula for a sphere : Volumes of Spheres and Other Solid Figures 6 Formula for volume of a sphere Substitute 10 for r.

Step 4 Multiply the volume of a single piece of gum in package 2 by 5 to get the total volume of gum in the package. (4189)(5) = 20,945 mm : Volumes of Spheres and Other Solid Figures 7

Step 5 Compare the volumes of the two packages to determine the best purchase. 10,480 < 20,945 The teenager should buy package : Volumes of Spheres and Other Solid Figures 8

Okay, here you go… Pictured to the right is a cylindrical grain silo. It can be completely filled to the top of the dome. The dome is in the shape of a hemisphere. The height of the silo is 300 feet to the top of the dome and the radius of the dome is 50 feet. How much grain can fit in the silo? Round to the nearest cubic foot : Volumes of Spheres and Other Solid Figures 9

thanks for watching! ms. dambreville