question_answer

From four corners of a rectangular iron sheet of\[\text{24 cm}\times \text{3}0\text{ cm}\], four squares of side 6 cm are cut. The remaining portion of the sheet is formed into an open box. The internal volume (in\[\text{c}{{\text{m}}^{\text{3}}}\]) of the box is

A)  4300

B)  2592

C)  2542

D)  1296  

Correct Answer: D

Solution :

 The base of the box (shaded portion in the diagram) has dimensions \[(24-2\times 6)\] by \[(30-2\times 6),\]i.e. \[12\text{ }cm\] by\[18\text{ }cm\]. Height of the box \[=6\text{ }cm\] \[\therefore \] Volume of the box \[=12\times 18\times 6=4296\text{ }c{{m}^{3}}\]