Question

a 40-lb container of peat moss measures 14x20x30 in. a 40-lb container of topsoil has a volume of 1.9 gal. (a) calculate the average densities of peat mass and topsoil in units of g/cm3. would it be correct to say that peat moss is "lighter" than topsoil? explain. (b) how many bags of the peat moss are needed to cover an area measuring 10 ft. by 20 ft. to a depth of 20 in.?

Answer 1

For the topsoil, it is 40 lbs/1.9 gallons assume US gallon. I US gallon = 3785ml. 1 kg=2.2 lbs so 1 lb = 1/2.2= 0.454 kg or 454 grams. 1.9 gallons = 3785 x 1.9 = 7192ml. 40 lbs=18160graams. So 18160/7192= 2.52 g/cc for the topsoil density. 
For the peat, the volume of the bag of the peat is 14x20x30 inches or 35.6x50.8x76.2cm (1 inch = 2/54 cm)= 137806 cc. So for the 40 lb again = 18160 grams/137806= 0.13 g/cc. So the peat is much lighter than the topsoil. 
As for the number of bags of peat needed to fill the given volume of 10ftx20ftx20 inches, the latter volume is 120"x240"x20"= 576,000 cubic inches and the volume of one bag is 14x20x30 inches= 8400 cubic inches so 576,000/8400= 68.6 bags of peat to fill it.