Library / UKMT Intermediate Mathematical Challenge /154 of 267

UKMT Intermediate Mathematical Challenge, 2026

Geometry Difficulty 2.0 Junior Find the answer United Kingdom

A cuboid has side-lengths, in cm, which are three consecutive positive integers. It has volume $120\text{ cm}^3$ . What is the area, in $\text{cm}^2$ , of its largest face?

(A) $15$ (B) $20$ (C) $24$ (D) $30$ (E) $41$

We don't reproduce this publisher's solutions. Their own solution is here — work the problem first.

Want a route through all this instead of an archive? The track puts 2,604 problems in a working order, from Junior Challenge level to the IMO shortlist.

Source: UK Mathematics Trust, licensed © UK Mathematics Trust; past papers published free at ukmt.org.uk. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.