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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?

Respuesta :

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

[tex]V_c=(\frac{1}{2})^3[/tex]

which gives

[tex]V_c=\frac{1}{8}ft^3[/tex]

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

[tex]V_s=2\frac{1}{2}\times2\times2[/tex]

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

[tex]2\frac{1}{2}=\frac{2\times2+1}{2}=\frac{5}{2}[/tex]

then, its volume is

[tex]\begin{gathered} V_s=\frac{5}{2}\times2\times2 \\ V_s=10ft^3 \end{gathered}[/tex]

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

[tex]\frac{V_s}{V_c}=\frac{10}{\frac{1}{8}}=80[/tex]

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

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