Constructing a cube with double the volume of another cube using only a straightedge and compass was proven possible by advanced algebra.A.TrueB.False

The statement is B. False.

Constructing a cube with double the volume of another cube using only a straightedge and compass is not possible due to the limitations of classical geometric construction. The volume of a cube is given by $V = s^3$, where $s$ is the length of a side. To double the volume of a cube, one would need to find a new side length $s'$ such that:

$s'^3 = 2s^3$

This implies:

$s' = s \times \sqrt[3]{2}$

The problem arises because $\sqrt[3]{2}$ is not a constructible number using just a straightedge and compass, as it cannot be expressed as a combination of integers and rational numbers through a finite series of operations (addition, subtraction, multiplication, division, and taking square roots).

Thus, we conclude the statement is false.