Question

question 23 of 25
it is possible to construct a cube of twice the volume of a given cube using only a straightedge and compass.
a. true
b. false

Explanation:

This is related to the classical problem of doubling the cube. It has been proven (using field - theory in algebra) that it is impossible to construct a cube with twice the volume of a given cube using only a straightedge and compass. The side - length of the new cube would need to be \(\sqrt[3]{2}\) times the side - length of the original cube. Since \(\sqrt[3]{2}\) is a non - constructible number (a number that cannot be constructed using only straightedge and compass operations which are equivalent to solving quadratic equations in the constructible number field), the construction is not possible.

Answer:

B. False