If each side of a cube is doubled, how does its volume change?

Introduction / Context:Volume scales with the cube of the linear dimension. If all edges of a 3D object are scaled by a factor k, the volume scales by k^3. Here, each side is doubled, so k = 2, and the new volume is 2^3 = 8 times the original.

Given Data / Assumptions:

• Original side length a.
• New side length = 2a.
• Volume formula for cube: V = a^3.

Concept / Approach:Compare V′ = (2a)^3 to V = a^3; the ratio V′/V reveals the multiplicative change.

Step-by-Step Calculation:V′ = (2a)^3 = 8a^3V′/V = 8a^3 / a^3 = 8

Verification / Alternative check:Try a = 1 ⇒ V = 1; doubling gives a = 2 ⇒ V′ = 8; ratio is 8, confirming.

Why Other Options Are Wrong:2x, 4x, and 6x correspond to squaring or linear misconceptions; volume scales with the cube of linear change.

Common Pitfalls:Confusing area scaling (k^2) with volume scaling (k^3).

Final Answer:Becomes 8 times