SOLUTION: The box holds twelve cans. The dimensions of the box are shown. Calculate the total volume of the twelve Cans. Length = 84 cm Width = 63 cm Height = 12 cm

Question 384590: The box holds twelve cans. The dimensions of the box are shown. Calculate the total volume of the twelve Cans.
Length = 84 cm
Width = 63 cm
Height = 12 cm
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
Let w = number of cans along the WIDTH,l = number of cans along the LENGTH, and z = number of cans along the HEIGHT. Also, let d = diameter of a can, and let h = height of can.
Then ld = 84, wd = 63, zh = 12, and lwz = 12. The first two equations give . Substituting this into lwz = 12, we get . The only integer values acceptable in the last equation are either {w = 1, z = 9}or {w = 3, z = 1}. The 1st set of values won't work, since we would get the equation 9l = 12, which has no integer solution for l. The 2nd set of values give the equation 3l = 12, which gives l = 4. Therefore the cans are arranged 3x4x1. The height of a can then is 12 cm, and the diameter is 21 cm, or a radius of 21/2 cm.
The volume of a can is then cubic cm. We get the total volume of the cans by multiplying by 12.
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