January 24th, 2018, 11:01 AM  #1 
Newbie Joined: Aug 2016 From: Pakistan Posts: 9 Thanks: 0  Problem
A closed box made of wood 1 cm thick, has external dimensions 20 cm by 15 cm by 10 cm. find the mass of the empty box if 1 cubic decimeter of wood weighs 1 kg?

January 24th, 2018, 12:09 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,116 Thanks: 1910 
If the box has internal dimensions 18 cm by 13 cm by 8 cm, the volume of the wood is (20×15×10  18×13×8) cm³ = 1.128 dm³. Does that help? 
January 24th, 2018, 12:12 PM  #3 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 895 
The simplest way to do this is to first calculate the volume of a 20 by 15 by 10 cm solid: 10(15)(20)= 3000 cubic cm. Then subtract off the 19 by 14 by 9 cm interior: 9(14)(19)=2394 cubic cm. The wood making up the box has volume 3000 2394= 606 cubic cm. A "decimeter' is 10 cm so a cubic decimeter is $10^3= 1000$ cubic cm so 606 cubic cm is 606/1000= 0.606 cubic decimeter. 