Question

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?

Answer 1

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.