Question

A metal sheet of thickness $2\text{cm}$ was used to make a container of external dimensions $30\text{cm}\times 15\text{cm}\times 25\text{cm}$ which is open from above. Find the volume of the container.

• A. $6578{\text{cm}}^3$
• B. $11250{\text{cm}}^3$
• C. $12250{\text{cm}}^3$
• D. $4672{\text{cm}}^3$

Answer 1

The correct option is D

$4672{\text{cm}}^3$

External volume of tank
$=30\text{cm}\times 15\text{cm}\times 25\text{cm}$
$=11250{\text{cm}}^3$

Internal dimensions
= External dimensions- 2 $\times$(thickness)

Since the tank is open from the top,
internal height
= External height - thickness
$\therefore$ Internal dimensions
$=(30-4)\times (15-4)\times (25-2)$
$=26\text{cm}\times 11\text{cm}\times 23\text{cm}$

Hence, inner volume $=26\text{cm}\times 11\text{cm}\times 23\text{cm}$
$=6578{\text{cm}}^3$

Hence, the volume of the container
$=\text{External volume of tank}-\text{internal volume of the tank}$
$=11250{\text{cm}}^3-6578{\text{cm}}^3$
$=4672{\text{cm}}^3$