Mark has a box that is 3 1/2 feet high, 4 2/7 feet wide and 5 feet long. Jeff has a box that measures 4 feet along each edge. Whose box has the greater volume? By how much?

1 Answer
Adam
Mar 15, 2018

Mark's box is larger by 11 cubic feet.

Explanation:

Determining the volume of the square is relatively simple so we'll start with that:
V_J = s^3
V_J = 4^3
V_J = 64 ft^3
To calculate the volume of a rectangular prism, we multiply length by width by height:
V_M = lwh
V_M = 5*4 2/7*3 1/2
V_M = 5*30/7*7/2
V_M = 1050/14
V_M = 75 ft^3
Find the difference:
V_D = V_M - V_D
V_D = 75-64
V_D = 11 ft^3
Therefore, Mark's box is larger by 11 cubic feet.

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