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MathNet 2026 — Part 01 Question 102

Math Olympiad Vault · MathNet 2026 — Part 01

Question 102

Three cylinders have heights and radii of the bases equal to $10~\mathrm{cm} \times 10~\mathrm{cm}$, $10~\mathrm{cm} \times 5~\mathrm{cm}$ and $20~\mathrm{cm} \times 5~\mathrm{cm}$, and volumes $V_{1}, V_{2}$ and $V_{3}$, respectively. Question illustration
a) Write in ascending order the volumes $V_{1}, V_{2}$ and $V_{3}$ of the three cylinders.
b) Give the dimensions of a cylinder $V_{4}$ whose volume is between $V_{2}$ and $V_{3}$.
c) Give the dimensions of a cylinder $V_{5}$ whose volume is between $V_{1}$ and $V_{3}$.