i need help with a conversion problem for chemistry?

Question

the problem is 5.25g/cm cubed and convert that to lbs./ft cubed.. can you solve it and help me how to do it? thanks

Answer 1

There are 2.54 cm/in, so there is (2.54)^3 = 16.4 cu cm/cu in.
There are 12 in/ft, so (12)^3 = 1728 cu in/cu ft.
There are 454 g/lb

5.25g/cu cm x [1lb/454g] x [16.4cu cm/cu in] x [1728cu in/1 cu ft] = (5.25)(16.4)(1728)/(454) = 328 lb/cu ft

The first factor converts lb and g. The g cancels, leaving lb/cu cm. The second factor converts cu cm and cu in. The cu cm cancels, leaving lb/cu in. The third factor converts cu in and cu ft. The cu in cancel, leaving lb/cu ft.

Answer 2

Conversions are always easier if you break them into a bunch of smaller problems. For this one we need to:

convert grams to pounds

convert cm to feet

using my spiffy converter, 1 cm = 0.0328 ft and 1 gram = 0.0022 lbs.

so if we do 5.25 X 0.0022 / 0.0328, we should get the right answer