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the packing crate below is 3 feet long and 2 1/4 feet wide. It is filled completely with 648 boxes that measure 1/4 foot on each side. What is the height, in feet, of the packing crate?

Guest Apr 19, 2017

#1
+2201
+1

the volume of one box = (1/4) * (1/4) * (1/4) = 1/64 cubic feet

the volume of all the boxes together = 648 * 1/64 = 10.125 cubic feet

the volume of the crate = the volume of all the boxes together

the volume of the crate = 10.125 cubic feet

the volume of the crate = 3 * 2.25 * height

10.125 = 3 * 2.25 * height

10.125 = 6.75 * height

10.125/6.75 = height

1.5 = height

height = 1.5 feet

hectictar Apr 19, 2017
Sort:

#1
+2201
+1

the volume of one box = (1/4) * (1/4) * (1/4) = 1/64 cubic feet

the volume of all the boxes together = 648 * 1/64 = 10.125 cubic feet

the volume of the crate = the volume of all the boxes together

the volume of the crate = 10.125 cubic feet

the volume of the crate = 3 * 2.25 * height

10.125 = 3 * 2.25 * height

10.125 = 6.75 * height

10.125/6.75 = height

1.5 = height

height = 1.5 feet

hectictar Apr 19, 2017

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