Scott is making a special box to hold an irregularly shaped statue with a volume of 1757 in3 for mailing. The box is a right triangular prism. If the height of the box is 30 inches while the sides of the bases are 12 inches, 16 inches, and 20 inches, how much packing material will fit around the statue?

Question

aaronq · Answer

The box looks like this |dw:1406943092701:dw|

aaronq · Answer

If you look carefully, we can complete this box into a full rectangular box, which would be equal to two of these. So the volume of the triangular box is HALF of the rectangular box.

|dw:1406943294740:dw|

The rectangular box has volume of $V_{rectangle}=30~in*16~in*12~in$

so the triangular box has the volume $V_{triangle}=\dfrac{1}{2}(30~in*16~in*12~in)$

The Volume of stuffing you can pack in the total volume of the box minus the volume of the statue (given in the question).

aaronq · Answer

The Volume of stuffing you can pack $\sf is^{**}$ the total volume of the box minus the volume of the statue (given in the question).