SOLUTION: A shipping box measures 14 1/2 inches long by 9 1/8 inches wide by 8 11/16 inches high. What is the volume of the box in cubic feet? Round to the nearest hundredth of a cubic foo

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A shipping box measures 14 1/2 inches long by 9 1/8 inches wide by 8 11/16 inches high. What is the volume of the box in cubic feet? Round to the nearest hundredth of a cubic foo      Log On


   



Question 152460: A shipping box measures 14 1/2 inches long by 9 1/8 inches wide by 8 11/16 inches high. What is the volume of the box in cubic feet? Round to the nearest hundredth of a cubic foot.
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
A shipping box measures 14 1/2 inches long by 9 1/8 inches wide by 8 11/16 inches high. What is the volume of the box in cubic feet? Round to the nearest hundredth of a cubic foot.

Change 141%2F2in to the decimal 14.5in
Change 91%2F8in to the decimal 9.125in
Change 811%2F16in to the decimal 8.6875in

V=LWH

V=%2814.5in%29%289.125in%29%288.6875in%29

V=%2814.5%29%289.125%29%288.6875%29%28in%5E3%29

V=1149.464844%28in%29%5E3

Now put this over 1

V=1149.464844%28in%29%5E3%2F1

Now we make a unit fraction, using
inches and feet that is a fraction 
that equals 1, that has equal
numerator and denominator, and which
will cancel away the inches. We know
that 12in=1ft. Therefore such a
unit fraction is %281%28ft%29%29%2F%2812%28in%29%29 

But we need to cancel away %28in%29%5E3,
so we cube the unit fraction and get
%281%5E3%28ft%29%5E3%29%2F%2812%5E3%28in%29%5E3%29 or
%281%28ft%29%5E3%29%2F%281728%28in%29%5E3%29

Now we multiply by that unit fraction:

V=%281149.464844%28in%29%5E3%2F1%29%28%281%28ft%29%5E3%29%2F%281728%28in%29%5E3%29%29

Now we can cancel the %28in%29%5E3



and all we have left is

V=%281149.464844%28ft%29%5E3%29%2F%281728%29

Divide that out and get:

V=0.6651995624ft%5E3

or to the nearest hundredth of a ft%5E3

V=0.67ft%5E3

Edwin