A rectangular prism is completely packed with 90 cubes of edge length 1/2 inch, without any gap or overlap. Which of the following describes the volume of this rectangular prism?
A: 11 unit cubes and 1 smaller cube of volume 1/8 cubic inch
B: 22 unit cubes and 4 smaller cubes of volume 1/8 cubic inch each
C: 11 unit cubes and 2 smaller cubes of volume 1/8 cubic inch each
D: 22 unit cubes and two smaller cubes of volume 1/8 cubic inch each
The answer is C: 11 cubes and 2 smaller cubes of volume 1/8 cubic inch each. Note that the volume of a cube is V=measurement of the side to the third power. Since one side measures 1/2 inch, we get the volume per cube as V=1/2 inch *1/2 inch * 1/2 inch = 1/8 cubic inch. For the total volume of the rectangular prism, V= no. of cubes* volume per cube; hence V= 90 cubes * 1/8 inch = 11 1/8 cubic inch. So we come up with the answer of letter C.
