IMAT 2013 Q27 [Safe Dimensions]

A safe has external dimensions as follows:

Width 48cm
Depth 44cm
Height 52cm

The entire safe is made of steel 4cm thick except the base which is 8cm thick.

What are the internal dimensions of the base of the safe?

A. 40cm x 40cm
B. 36cm x 36cm
C. 40cm x 32cm
D. 44cm x 40cm
E. 40cm x 36cm

Simple steps to solve word problems:

  • Underline key information
  • Determine what they are trying to ask, and what you will need to solve it
    • Eliminate any non-essential information
  • Draw a picture, graph, or equation
    • In moments of high stress like exam taking, always work with the paper they give you to avoid careless mistakes.
  • Solve.

The best way to approach this problem is to take the information given and then make a quick sketch. The important thing to know is that we are looking for the interior surface area of the base, meaning we only need to work with width and depth because height does not contribute to this surface area. The next important step is to figure out what is meant by the walls and the base because we need to know which is 4cm thick and what is 8cm. The thickness of the walls is determined by the length and width, while the height determines the thickness of the base and roof (easier to see in the drawing). We can now eliminate the 8cm base thickness clue given to us in the question because it applies to height, which is not needed in our calculations.

Steps to solve: Find the base’s width by subtracting the total width minus the thickness of both sets of walls (there are walls on all sides). Next, do the same with the depth.

\fcolorbox{red}{grey!30}{Therefore the answer is E, $40$cm x $36$cm.}