SOLUTION: A metal worker is building a wire frame (represented by the dotted and solid lines in the diagram above) for a cubic box that is to have a volume of 27 cubic feet. What is the to

Algebra ->  Equations -> SOLUTION: A metal worker is building a wire frame (represented by the dotted and solid lines in the diagram above) for a cubic box that is to have a volume of 27 cubic feet. What is the to      Log On


   

Question 86100: A metal worker is building a wire frame (represented by the dotted
and solid lines in the diagram above) for a cubic box that is to have
a volume of 27 cubic feet. What is the total length of wire the metal
worker will need?
A. 27 feet
B. 36 feet
C. 54 feet
D. 81 feet
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
The volume of cube can be found using this formula:

s%5E3=V where s is the length of the side and V is the volume

So if we know the volume is 27, this means V=27

s%5E3=27 Plug in V=27


root%283%2Cs%5E3%29=root%283%2C27%29 Take the cube root of both sides (this undoes the exponent)



s=3 Use your calculator to evaluate the cube root of 27

So the length of the side is 3 feet. Now lets count the number of segments. There are 12 segments that form the cube. So if we multiply 12 by 3 we'll get the total perimeter of the cube. It turns out that the perimeter of a cube is

P=12s

P=12%283%29

P=36

So the perimeter of the cube is 36. So the answer is B)