A box is in the shape of a cuboid. Its smallest side is 30 cm and its largest side is 60 cm. Which of the following can be the volume (in cm3) of the box?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 81000
The third side lies between the smallest and the largest side, so the volume lies between \(30\times30\times60\) and \(30\times60\times60\).
Least volume (middle side 30 cm): \(30\times30\times60=54000\) cm3
Greatest volume (middle side 60 cm): \(30\times60\times60=108000\) cm3
\(81000=30\times45\times60\): the middle side 45 cm lies between 30 cm and 60 cm, so this volume is possible
Why the other options are incorrect
Option (1) 45000 — Incorrect. It is less than 54000, so the middle side would be \(45000\div1800=25\) cm, shorter than the smallest side.
Option (2) 120000 — Incorrect. It is more than 108000, so the middle side would be \(120000\div1800\approx66.7\) cm, longer than the largest side.
Option (3) 50000 — Incorrect. It is less than 54000, so the middle side would be about 27.8 cm, shorter than the smallest side.