Question

each cube inside the rectangular prism has an edge length of $\frac{1}{3}$ yard. what is the volume of the rectangular prism?

Explanation:

Step1: Calculate volume of one small cube

The volume formula for a cube is $V = s^3$, where $s$ is the side - length. Given $s=\frac{1}{3}$ yard, so $V_{cube}=(\frac{1}{3})^3=\frac{1}{27}$ yd³.

Step2: Count number of small cubes

By counting (assuming the dimensions of the rectangular prism in terms of the number of small - cube side - lengths), if we assume the rectangular prism has dimensions $l\times w\times h$ in terms of the number of small - cube side - lengths. Let's assume it has $9\times3\times7$ small cubes (by visual inspection). The total number of small cubes $n = 9\times3\times7=189$.

Step3: Calculate volume of rectangular prism

The volume of the rectangular prism $V_{prism}=n\times V_{cube}$. Substitute $n = 189$ and $V_{cube}=\frac{1}{27}$ into the formula: $V_{prism}=189\times\frac{1}{27}=21$ yd³.

Answer:

21 yd³