Question

1. (01.07 mc) a rectangular prism is completely packed with 54 cubes of edge length 1/2 inch, without any gap or overlap. which of these best describes the volume of this rectangular prism? (1 point) 6 unit cubes and 6 smaller cubes of volume 1/8 - cubic inch each 13 unit cubes and 4 smaller cubes of volume 1/8 - cubic inch each 6 unit cubes and 3 smaller cubes of volume 1/8 - cubic inch each 13 unit cubes and 2 smaller cubes of volume 1/8 - cubic inch each

Explanation:

Step1: Calculate volume of one small - cube

The volume of a cube with edge length $a$ is $V = a^{3}$. Given $a=\frac{1}{2}$ inch, so $V_{1}=(\frac{1}{2})^{3}=\frac{1}{8}$ cubic inch.

Step2: Calculate volume of the prism

The prism is packed with 54 such cubes. The volume of the prism $V_{p}$ is the number of cubes times the volume of one cube. So $V_{p}=54\times\frac{1}{8}=\frac{54}{8}=\frac{27}{4} = 6\frac{3}{4}$ cubic inches. This is equivalent to 6 unit - cubes (each of volume 1 cubic inch) and 6 smaller cubes of volume $\frac{1}{8}$ cubic inch each since $6\times1 + 6\times\frac{1}{8}=6+\frac{6}{8}=6\frac{3}{4}$.

Answer:

6 unit cubes and 6 smaller cubes of volume $\frac{1}{8}$ cubic inch each