A rectangular prism is completely packed with 180 cubes of edge length fraction 1 over 3 inch, without any gap or overlap. Which of the following describes the volume of this rectangular prism?

19 unit cubes and 9 smaller cubes of volume fraction 1 over 27 cubic inch each
19 unit cubes and 27 smaller cubes of volume fraction 1 over 27 cubic inch each
6 unit cubes and 6 smaller cubes of volume fraction 1 over 27 cubic inch each
6 unit cubes and 18 smaller cubes of volume fraction 1 over 27 cubic inch each

Question

A rectangular prism is completely packed with 180 cubes of edge length fraction 1 over 3 inch, without any gap or overlap. Which of the following describes the volume of this rectangular prism?

 19 unit cubes and 9 smaller cubes of volume  fraction 1 over 27 cubic inch each
 19 unit cubes and 27 smaller cubes of volume fraction 1 over 27 cubic inch each
 6 unit cubes and 6 smaller cubes of volume fraction 1 over 27 cubic inch each
 6 unit cubes and 18 smaller cubes of volume fraction 1 over 27 cubic inch each

mertsj · Answer

$$V=180(\frac{1}{3})(\frac{1}{3})(\frac{1}{3})$$