A box is in the shape of a cuboid. Its smallest side is 40 cm and its largest side is 80 cm. Which of the following can be the volume (in cm3) of the box?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 175000
The third side lies between the smallest and the largest side, from 40 cm to 80 cm, so the volume lies between the two extreme cases.
Volume \(=40\times80\times x=3200x\), with \(40\le x\le80\)
Least volume \(=3200\times40=128000\) cm3
Greatest volume \(=3200\times80=256000\) cm3
Only 175000 lies between 128000 and 256000; it needs \(x=175000\div3200=54.6875\) cm, which is allowed
Why the other options are incorrect
Option (1) 265000 — Incorrect. It is above 256000; the third side would be about 82.8 cm, longer than the largest side.
Option (2) 115000 — Incorrect. It is below 128000; the third side would be about 35.9 cm, shorter than the smallest side.
Option (4) 375000 — Incorrect. It is far above 256000; the third side would be about 117 cm.