Cube root, finding the length of the wire around a cube

Question

A piece of wire is used to form the framework of a cube the volume of the cube is 2744 cubic inches find the length of the wire

Answer 1

The problem gives the volume of the cube as 2744 in3.
The volume of a cube is V=s3  where s = length of side,  and  V = volume
For this problem, the Volume is 274 in3, so the side length is 13 in.
 
A cube has 6 faces, each square.  But squares share sides in a cube, so if this cube shape is made by using wire, the number of sides required is 12  (PLZ carefully count them).
 
This means that a cube with side 14 in requires 12*14 in = 168 inches of wire

Answer 2

For a cube of side length s:

 

Volume = s³

 

³√(Volume) = s

 

³√2744 = 14 inches

 

Each side (edge) of the cube is 14 inches long  There are 12 edges in a cube, so the wire needs to be 12*14 = 168 inches long.

Answer 3

The wire forms the cube.  A cube has side lengths that are equal all around.  The volume of a cube is the cube of the side length.

 

 

Let x = sides of cube

 

V = x³

 

2744 = x³

 

 

Cube root both sides if the equation.

 

³√(2744) = x

 

14 = x

 

 

The cube has side lengths of 14 inches.  We know that a cube is made up of squares.  4 pieces of wire will make the 1st square.  Another 4 pieces will make the 2nd square.  These two squares are parallel to each other.  Now, if we add 4 more pieces, we can use each of those pieces to connect the two squares at their corners.  This completes the wireframe of the cube.

 

We have 3 sets of 4 pieces,  so we have 12 pieces of wire in total.

 

 

Wire length = 14 inches × 12

Wire length = 168 inches