Expert: Abe Mantell - 8/2/2011

Question
a solid cube with edge of 10 cm. will be ccovered with paint 1/2 mm thick. find the approximate volume of paint needed in cubic meters

Answer
The 6 faces are each 10 by 10 or 100 cm^2.  So the paint covering them will have
a volume of 0.05(100) cm^3, since 1/2 mm = 0.05 cm.  So the volume per side is
5 cm^3...for all 6 sides is 6(5 cm^3)=30 cm^3.

But we have the volume of paint on the edges as well!  If you can picture the paint
on the edges, they are roughly 0.05 cm by 0.05 cm by 10 cm = 0.025 cm^3, times 12 edges
gives 12(0.025 cm^3) = 0.3 cm^3.

Then we have the 8 corners of paint volume!  Each corner of paint is roughly
0.05 cm by 0.05 cm by 0.05 cm = 0.000125 cm^3, times 12 gives 0.0015 cm^3.

So the total volume is about 30+0.3+0.0015 = 30.3015 cm^3

If you want m^3, then divide this by 100^3, since 1 meter = 100 cm.
So, in m^3, the volume is about 0.0000303015 m^3.

Abe