Verified Answer :

vadimbur

Doubled: Volume increased 8 times 
Tripled: Volume increased 27 times 
Quadrupled: Volume increased 64 times 

Pretty simple... if you're doubling the lengths, you're increasing them by 2 times. Take 2 and raise it to the 3rd power. If you're tripling the lengths, you're increasing them 3 times over. Take 3 and raise it to the 3rd power. And so on. 

Doubled = 2^3 = 8 
Tripled = 3^3 = 27 
Quadrupled = 4^3 = 64 

Does that make sense?

Answer:

The new volume of the larger cube becomes eight times of the smaller cube.

Step-by-step explanation:

Let the edge of the cube be x.

Volume of cube = V = \(x^3\)..[1]

If we double the edge of the cube, then edge of the cube becomes = 2x

The volume of cube whose edges are doubled = V'

\(V'=(2x)^3=8x^3\),..[2]

Dividing [1] and [2]:

\(\frac{V}{V'}=\frac{x^3}{8x^3}\)

\(V'=8\times V\)

The new volume of the larger cube becomes eight times of the smaller cube.

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