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

Answer:

D) 4176 unit cubes

Step-by-step explanation:

Length of the right rectangular prism $=7\frac{1}{4}$ 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)

$=\left(7\frac{1}{4}\right)\left(8\right)\left(9\right)$

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

$=522$ cubic inches

Now volume of the small cubic prism $=(Length)^3=\left(\frac{1}{2}\right)^3=\frac{1}{8}$

Then number of cubes that can fit into the right rectangular prism $=\frac{522}{\left(\frac{1}{8}\right)}=522*8=4176$

Hence correct choice is D) 4176 unit cubes