Final Jeopardy

The math team receives a 9”x12”x18” plastic shipping container in the shape of a right rectangular prism.  The shipping container is perfectly filled with neatly stacked bouncy balls.  (There is no issue with any deflated balls in this case.) The noncompressable bouncy balls have a radius of .25” each.  (Each row and column of balls is making contact with either the ball beside it or the actual container.  Each row is parallel with the next row and each column is parallel with the next column.)When the container is opened, the volume not consumed by the bouncy balls is filled with sand.  The sand is removed and placed into containers in the shape of a right circular cylinder.  The cylinders are 5” tall with a radius of 3”.  If each cylinder is filled, what percentage of the last cylinder is filled? (Please round to the nearest percent.)

Final Jeopardy Answer

Box

3Box

Box :9"x12"x18"

Vol = 9 x12 x18

Vol 1944in3

Ball

3Ball

3Balls

Balls :18x 24 x 36 = 15,552balls

4Vol

34

Vol 3.14 0.25 0.0654163

Vol = 15,552balls 0.065416 1017.36

r

x in

3

Volof thesand = Vol of box Volof Balls

Vol of thesand = 1944 1017.36

Vol of thesand 926.64in

2cylinder

2cylinder

3cylinder

Vol

Vol 3.14 3 5

Vol 141.3

r h

in

sand cylinderNumber of cylinders = Vol ÷ Vol

Number of cylinders = 926.64 141.3

6.56 cylinders needed

0.56 of the last cylinder is filled:

This is 56% of that cylinder's volume.

56%