Three balls are packaged in a cylindrical container as shown below. If the balls just touch the top, bottom, and sides of the cylinder, and the diameter of a single ball is 7 centimeters, how much of the space inside the cylinder is not filled by the balls? Use 3.14 = π and round your answer to the nearest cubic centimeter.For 1 Point(s)

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Answer:

A) 269 cubic centimeters
B) 279 cubic centimeters
C) 291 cubic centimeters
D) 297 cubic centimeters

First you have to find the volume of the sphere which is found with the formula (4/3 (3.14) r^3). The diameter is given to you but you need the radius so half of 7 is 3.5. Inputting that into a calculator gives you 179.59. You then multiply by 3 because there are 3 balls which gives you 538.77. Now that you have the volume of the ball you subtract that by the volume of the cylinder. The formula for cylinder is ((3.14) r^2 h). We can find the height of the balls by multiplying the diameter of the balls by 3 which gives you 21. The radius is is still 3.5. Solving it gives you 808.17. Now that you know the volumes, you subtract the volume of the balls (538.77) from the cylinder (808.17). You get 269.4 which you round and get 269.