Question

Can a Cube be constructed using straight edge and compass that has double the volume of another cube?

• A. Yes
• B. No
• C. Not always

Answer 1

The correct option is B No

No, it's not possible to construct a cube using straight edge and compass that has double the volume of another cube.

Imagine a cube of unit length.



Volume = $a^3$
$a=1$
Volume = $1\times 1\times 1$ = 1 unit${}^3$

Now we have to produce a cube of double the Volume.


Given that particular length of one of the side produce double the volume. No, it is impossible in general.

If first cube is a unit cube then what would the cube we need to construct so that it's volume is 1.

Heres the volume = $1\times 1\times 1$
V = $a^3$
$a=1$ unit
V = 1 unit${}^3$

$\therefore$ the volume of another cube will have to be 2 . So each side has to be cube root of 2 units.


V = $s^3$
$s=2^{\left(\frac{1}{3}\right)}$ unit
V = 2 unit${}^3$

Because it is 3rd power it cannot be constructed.
Since it cannot be expressed in powers of 2 it is impossible .