A close box made of wood 1cm thick has ecteenal dimensions 20cm by 15cm by10 cm.find the mass of the empty box.if one cubid decimeter of wood weight 1kg?

Here's what I got.

The idea here is that you need to determine the volume of the wood needed to make the box. To do that, you will have to consider two boxes

• an "outside" box with the dimensions given to you in the problem
• an "inside" box with the dimensions that take into account the wood's thickness

The volume of the wood used to make the box will be the diference between these two volumes.

##V_"wood" = V_"outside" - V_"inside"##

I assume that "ecteenal" is actualy external. The volume of the outside box will be

##V_"outside" = "20 cm" xx "15 cm" xx "10 cm" = "3000 cm"^3##

Now, since the wood is ##"1 cm"## thick, it follows that the inside of the box will have the following dimensions - keep in mind that you need to take thickness into account on both sides of the box!

##V_"inside" = [20-(1+1)]"cm" xx [15 - (1+1)]"cm" xx [10-(1+1])"cm"##

##V_"inside" = "18 cm" xx "13 cm" xx "8 cm" = "1872 cm"^3##

The volume of the wood will thus be

##V_"wood" = "3000 cm"^3 - "1872 cm"^3 = "1128 cm"^3##

Convert this value to cubic decimeters to make it match the units you have for the of wood

##1128color(red)(cancel(color(black)("cm"^3))) * "1 dm"^3/(10^3color(red)(cancel(color(black)("cm"^3)))) = "1.128 dm"^3##

Now use the given to find the mass of this volume of wood

##1.128color(red)(cancel(color(black)("dm"^3))) * "1 kg"/(1color(red)(cancel(color(black)("dm"^3)))) = "1.128 kg"##

I'll leave the answer rounded to two

##m_"box" = color(green)("1.1 kg")##