Question

dana helped her dad build a sandbox for her younger sister. the sandbox is shaped like a rectangular prism that is 4 1/2 feet long and 4 feet wide. dana used bags of sand to fill the sandbox 1/2 of a foot deep. each bag contained 1/2 of a cubic foot of sand. how many bags of sand did dana use?

Explanation:

Step1: Calculate the volume of the sandbox

The volume $V$ of a rectangular prism is $V = l\times w\times h$, where $l = 4\frac{1}{2}=\frac{9}{2}$ feet, $w = 4$ feet and $h=\frac{1}{2}$ foot. So $V=\frac{9}{2}\times4\times\frac{1}{2}$.
$V=\frac{9\times4\times1}{2\times2}=\frac{36}{4} = 9$ cubic - feet.

Step2: Calculate the number of sand - bags

Each bag contains $\frac{1}{2}$ cubic - foot of sand. Let the number of bags be $n$. Then $n=\frac{V}{\text{Volume per bag}}$. Since $V = 9$ cubic - feet and volume per bag is $\frac{1}{2}$ cubic - foot, $n=\frac{9}{\frac{1}{2}}=9\times2 = 18$.

Answer:

18