Question

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)

Answer 1

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.

Step-by-step explanation:

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

`\begin{gathered} Volume=l* b* h \\ =10.5*5*2 \\ =105in^3 \end{gathered}`

Since the edge length of 0.5inch.

Then,

`\begin{gathered} Volume\text{ of rectangular prism}=n* Volume\text{ of a cube} \\ 105=n*(0.5)^3 \\ n=(105)/(0.125) \\ n=840 \end{gathered}`

Hence, the number of cubes is 840 unit cubes.