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
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.