Question

A closed rectangular box is made of wood of $1.5$ cm thickness. The exterior length and breadth are respectively $78$ cm and $19$ cm and the capacity of the box is $15$ cubic decimetres. Calculate the exterior height of the box.

• A.
  $15.5$ cm
• B. $13$ cm
• C. $19$ cm
• D. $17.5$ cm

Answer 1

Answer: (A)

$15.5$ cm

Given, the external dimensions of a closed wooden box are $78$ cm, $19$ cm.

Let the external height be $h$ cm respectively.

As the thickness is $1.5$ cm , the internal length, breadth and height of the closed box are $78-2\left(1.5\right)=75$ cm, $19-2\left(1.5\right)=16$ cm
and $h-2\left(1.5\right)=(h-3)$ cm respectively.
Given, capacity of the box $=15cudm=15000cucm$

As the box is cuboidal, its volume $=$ length $\times$ breadth $\times$ height

$\Rightarrow (75\times 16\times (h-3\left)\right)=15000$

$\Rightarrow (h-3)=12.5$ cm

$\Rightarrow h=15.5$ cm