The side of the edge of the cube is 9. 9cm
<h3>How to determine the length</h3>
Given that the diagonal of a cube measures the square root of 294cm and the diagonal of a face measures 14cm
To find the edge of the face, we know that the face of the cube is a square
Formula for diagonal of a square = 
Where is the side of the square
We then have,

Make 'a' the subject
a = 
Simplify the surd
a =
× 
a = 
a = 
a = 9. 9cm
Therefore, the side of the edge of the cube is 9. 9cm
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The length, width and height of the rectangular prism is ∛10
<h3>How to determine the dimensions?</h3>
The volume is given as:
Volume, V = 10m^3
For a minimised volume, we have:
Length = Width = Height
This means that:
V = L^3
So, we have:
L^3 = 10
Take the cube root of both sides
L = ∛10
Hence, the length, width and height of the rectangular prism is ∛10
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Answer:
Roughly 376.99 cm(If im doing this right.
Step-by-step explanation:
The additive inverse of 1/3 is 3/1.
Hope this helps you!
:)