Suppose that ten chips, numbered 1 through 10, are put into an urn at one minute to midnight, and chip number 1 is quickly removed. at one-half minute to mid-night, chips numbered 11 through 20 are added to the urn, and chip number 2 is quickly removed. then at one-fourth minute to midnight, chips numbered 21 to 30 are added to the urn, and chip number 3 is quickly removed. if that procedure for adding chips to the urn continues, how many chips will be in the urn at midnight (157)?

The volume of the composite figure is 263.76 inches³

Step-by-step explanation:

The volume of a cylinder of radius r and height h is

V = πr²h ⇒ Bh

The volume of a cone of radius r and height h is

V =  πr²h ⇒  Bh

The volume of a sphere with radius r is

V =  πr³

∵ The figure is made up of a cylinder, a cone, and a half sphere

∵ The radius of the cylinder = 3 inches

∵ The height of the cylinder = 6 inches

∵ π = 3.14

- Use the rule of the volume of the cylinder above

∴ The volume of the cylinder = (3.14)(3)²(6)

∴ The volume of the cylinder = 169.56 inches³

∵ The radius of the cone = 3 inches

∵ The height of the cone = 4 inches

∵ π = 3.14

- Use the rule of the volume of the cone above

∴ The volume of the cone =

∴ The volume of the cone = 37.68 inches³

∵ The radius of the half sphere = 3 inches

∵ π = 3.14

- Use the rule of the volume of the sphere above to find the

  volume of the half sphere

∴ The volume of half sphere =

∴ The volume of half sphere = 56.52 inches³

To find the volume of the composite figure add the volumes of the three shapes above

∵ The volume of the composite figure = 169.56 + 37.68 + 56.52

∴ The volume of the composite figure = 263.76 inches³

The volume of the composite figure is 263.76 inches³

Step-by-step explanation:

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