Question

a 40-lb container of peat moss measure 14x20x30 inches and has an average density of 0.13 g/cm^3. how many bags of peat moss are needed to cover an area measure 1 3ft by 25 ft to a depth of 1.9 inches?

Answer 1

Volume of the peat moss = $14\times 20\times 30 inches$

= $8400 in^{3}$

Convert the above volume into $cm^{3}$

$1 in^{3}= 16.4 cm^{3}$

Thus, volume in $cm^{3}$ is:

Volume of peat moss =  $8400 in^{3}\times \frac{16.4 cm^{3}}{1 in^{3}}$

= $137760 cm^{3}$

Now,

Total volume by using area and depth of the peat moss = $area of peat moss \times depth of peat moss$

= $(13 ft \times  25 ft)\times 1.9 inches$

= $(325 ft^{2})\times 1.9 inches$

Convert above values in $cm$ to get the value of volume in $cm^{3}$:

$1 ft= 30.48 cm$

$1 in= 2.54 cm$

Thus, volume in $cm^{3}$ is:

Total volume = $(325 ft^{2}\times\frac{(30.48 cm)^{2}}{(1 ft)^{2}})\times (1.9 in\times \frac{2.54 cm}{1 in})$

= $301934.88 cm^{2}\times 4.826 cm$

= $1457137.73088 cm^{3}$

Now, number of bags is calculated by the ratio of total volume of the peat moss to the volume of the peat moss.

$Number of bags  =\frac{total volume of peat moss}{volume of peat moss}$

Substitute the values of volume in above formula:

$Number of bags  = \frac{1457137.73088 cm^{3}}{137760 cm^{3}}$

= $10.57$

≅ $11$ bags

Thus, number of bags of peat moss are needed to cover an area measure $13 ft$ by $25 ft$ to a depth of $1.9 inches$ are $11$ bags.