Question

Alan is a paleontologist who collects dinosaur fossils. He keeps each fossil in a cube - shaped box with edges that are 1/2 ft long. Alan keeps the boxes in a storage bin. The storage bin is a right rectangular prism that is 2 1/2 ft. long, 2 ft. wide, and 2 ft. tall. How many boxes can Alan keep in the bin?

Answer 1

In order to answer this question, we need to find the volume of one cubic box and the volumeof the storage bin.

The volume of the cubic box is given by

`V_c=((1)/(2))^3`

which gives

`V_c=(1)/(8)ft^3`

On the other hand, the volume of the storage bin is given by

`V_s=2(1)/(2)*2*2`

but we need to convert first the mixed fraction form into a simple fraction form, that is

`2(1)/(2)=(2*2+1)/(2)=(5)/(2)`

then, its volume is

`\begin{gathered} V_s=(5)/(2)*2*2 \\ V_s=10ft^3 \end{gathered}`

Now, we need to compare our last volume with the volume of the cubic box, that is,

`(V_s)/(V_c)=(10)/((1)/(8))=80`

this means that Alan can keep 80 cubic boxes into the storage bin