Question

If the length of the side of a cube is doubled, and he the ratio of the volumes of new cube and the original cube is

Answer 1

Let x be the original length of the side.

After it is doubled, the length is 2x.

Volume = Length³

Original volume = x³

New volume = (2x)³ = 8x³

Answer: The volume has increased 8 times.

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Alternative method:

The increase in volume is the cube of the increase in length

⇒ length is doubled

⇒ length is increase to 2 times

⇒ volume increased to (2)³ = 8 times

Answer: The volume has increased 8 times.

Answer 2

$\mathfrak{Answer:}$

= 8 : 1

$\mathfrak{Step-by-Step\:Explanation:}$

Let the length of the side of the cube be x cm.

$\\\\\underline{\textbf{In first case we have:}}\\\\\\\bullet\bold{\:The\:side\:of\:the\:cube=x\:cm.}\\\\\\ \boxed{\bold{Volume\:of\:cube=(side)^3.}}\\\\\\\tt{=(x\:cm)^3}\\\\\\\tt{=x^3\:cm^3.}\\\\\\\underline{\textbf{In second case we have:}}\\\\\\\bullet\bold{\:The\:side\:of\:the\:cube=2\times x=2x\:cm.}\\\\\\\bold{Volume=(side)^3}\\\\\\\tt{=(2x\:cm^3)}\\\\\\\tt{=8x^3\:cm^3.}\\\\\\\tt{So}\\\\\\\bold{The\:ratio\:of\:volume:}\\\\\\\tt{New\:volume:Original\:volume}$

$\tt{=(8x^3\:cm^3):(x^3\:cm^3)}\\\\\\\tt{=8:1}.$