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A right rectangular prism's edge lengths are 10.5 inches, 5 inches, and 2 inches. How many unit cubes with edge lengths of 0.5 inch can fit inside the prism?A)105 unit cubesB)210 unit cubes460 unit cubesD)840 unit cubes5)

Sagot :

Given

A right rectangular prism's edge lengths are 10.5 inches, 5 inches, and 2 inches.

To find how many unit cubes of edge length 0.5 inches can fit inside the prism.

Explanation:

It is given that, the volume of the rectangular prism is,

[tex]\begin{gathered} Volume=l\times b\times h \\ =10.5\times5\times2 \\ =105in^3 \end{gathered}[/tex]

Since the edge length of 0.5inch.

Then,

[tex]\begin{gathered} Volume\text{ of rectangular prism}=n\times Volume\text{ of a cube} \\ 105=n\times(0.5)^3 \\ n=\frac{105}{0.125} \\ n=840 \end{gathered}[/tex]

Hence, the number of cubes is 840 unit cubes.

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