Zoox·Machine Learning Engineer·Technical Phone Screen·Senior

Senior

Apr 2026

Summary

Zoox ML Engineer interview had at least one math-heavy question that felt more like a physics class than a machine learning screen. Not bad, just unexpected.

Questions Asked (1)

Sphere A has radius r and Sphere B has a radius 50% larger. Given the volume of A, calculate the volume of B by hand and explain why volume scales as the cube of the radius.

Technical Trade-offsAlgorithms & Data Structures

Author's notes

I knew the cube relationship but fumbled spelling out 1.5 cubed cleanly without a calculator.

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AI HintsAI Generated

Suggested Approach

First, compute the new radius as 1.5r, then calculate the volume ratio by cubing the scale factor (1.5^3 = 3.375) and multiply by the original volume. Explain that volume scales with the cube of the radius because volume is a three-dimensional measure, so each dimension scales linearly with the radius.

Pro tip: Connect the concept to machine learning by mentioning how scaling laws (e.g., model size vs. performance) often follow power laws, and that understanding dimensional scaling is crucial for reasoning about data and model complexity.

1. Identify the scale factor

Determine the new radius: if Sphere B's radius is 50% larger, then r_B = r_A * 1.5.

2. Recall the volume formula

State the volume of a sphere: V = (4/3)πr^3. This shows volume depends on the cube of the radius.

3. Compute the volume ratio

Calculate the ratio V_B / V_A = (r_B / r_A)^3 = (1.5)^3 = 3.375. So V_B = 3.375 * V_A.

4. Explain the cubic scaling

Explain that volume is a three-dimensional quantity: scaling the radius by a factor k scales volume by k^3 because each of the three spatial dimensions scales by k.

5. Relate to ML context

Mention that similar scaling principles apply in ML, e.g., how the number of parameters or compute scales with model size, often following power laws.

Key Points to Mention

Volume of a sphere formula: V = (4/3)πr^3
Scale factor: 1.5 (since 50% larger means 1 + 0.5 = 1.5)
Cubic scaling: (1.5)^3 = 3.375
Dimensional analysis: volume is 3D, so it scales with the cube of linear dimensions
General principle: for similar shapes, volume scales as the cube of any linear dimension
Connection to ML: scaling laws and power-law relationships in model performance

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.