Question: Cube 1 has side (ell_{1}) and volume (V_{1}). Cube 2 has side (ell_{2}=2 ell_{1}). (a) When making order-of-magnitude estimates, by how many orders of magnitude

Cube 1 has side $\ell_{1}$ and volume $V_{1}$. Cube 2 has side $\ell_{2}=2 \ell_{1}$.

(a) When making order-of-magnitude estimates, by how many orders of magnitude is the volume of the second cube greater than the volume of the first cube?

(b) Does the answer depend on the numerical value of $\ell_{1}$ ?

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