Question

Dry sand has a density of 1.5 g cm^-3. A child’s sandbox measuring 4.0ft by 5.0ft, is filled with sand to a depth of 6.0in. What is the mass of the sand in kg? In lb?

Answer 1

Dry sand has a density of $1.5\mathrm{g/cm^3}$. A child's sandbox measuring 4.0ft by 5.0ft, is filled with sand to a depth of 6.0in. What is the mass of the sand in kg? In lb?

Solution:

Let's calculate sandbox volume first:

V = 4ft * 5ft * 0.5ft = 10ft³

(1 foot equals to 12 inches, so 6 inches = 0.5ft)

One foot = 30.48 cm, so 1 cubic foot equals to $(30.48\mathrm{cm})^3 = 28316.8\mathrm{cm}^3$, so $10ft^3$ are equal to $283168\mathrm{cm}^3$.

Then, sandbox filled with mentioned volume of sand will contain such mass of sand:

m = ρ * V = 1.5 g/cm³ * 283168 cm³ = 424752 g = 424.752 kg

(where $\rho$ - is density of sand, V - volume of sand).

One kilogram approximately equals to 2.20 pounds, so 424.752 kilograms of sand will weight $424.752\mathrm{kg}^* 2.20 = 934.4544\mathrm{lb}$

Answer:

Sandbox with dimensions mentioned in task will contain $424.752\mathrm{kg}$ or 934.4544 lb of sand.