Average Sample Problem
Step 4

Step 4

Set up the solution--check units.

The problem

The Berliner Lecture Room (PSB 180) at Bryn Mawr College is approximately 42.8 feet long by 26.3 feet wide by 11.6 feet tall. This room is filled with cubic blocks. Each block is 0.75 cm/side and has a mass of 15 grams. The room is filled with blocks. What would be the total mass of the blocks required to fill the room (assume partial blocks may be obtained).

You may be thinking...

This problem asks for a mass, yet most of the information given is length. Working backwards, consider:
  1. Each block has a mass of 15 grams
  2. Find the number of blocks to fill the room, multiply by the mass to get total mass.
  3. Find the volume of the room in feet3, convert to cm3 and then divide by the volume of one block to find the number of blocks to fill the room.
To find the volume of the room, multiply length times width times height and then do the conversion to cm3. Divide the total volume by the volume of one block (multiply by the reciprocal) to get the total number of blocks in the room and then multiply by the mass of a single block

Check units

Note: If the conversion factors were not cubed, the units would be incorrect. Checking the units before doing the calculation will often alert you to these types of errors.

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