Question

A right rectangular prism's edge lengths are 7 1/ 4 inches, 8 inches, and 9 inches. How many unit cubes with edge lengths of 1 2 inch can fit inside the prism? A) 224 unit cubes B) 940 unit cubes C) 1360 unit cubes D) 4176 unit cubes

Answer 1

D) 4176 unit cubes

Explanation:

Length of the right rectangular prism
`=7(1)/(4)` inches

Width of the right rectangular prism
`=8` inches

Height of the right rectangular prism
`=9` inches

Then volume of the right rectangular prism = (Length)(Width)(Height)

`=\left(7(1)/(4)\right)\left(8\right)\left(9\right)`

`=\left(7.25\right)\left(8\right)\left(9\right)`

`=522` cubic inches

Now volume of the small cubic prism
`=(Length)^3=\left((1)/(2)\right)^3=(1)/(8)`

Then number of cubes that can fit into the right rectangular prism
`=(522)/(\left((1)/(8)\right))=522*8=4176`

Hence correct choice is D) 4176 unit cubes