Question

what is the volume of the rectangular prism?
1/3 ft
1 1/9 ft³ 3 1/3 ft³ 2/9 ft³ 10 ft³

Explanation:

Step1: Calculate the volume of one small cube

The side length of one small cube is $\frac{1}{3}$ ft. The volume of a cube is $V = s^3$ (where $s$ is the side - length). So, $V_{cube}=(\frac{1}{3})^3=\frac{1}{3}\times\frac{1}{3}\times\frac{1}{3}=\frac{1}{27}$ $ft^3$.

Step2: Count the number of small cubes in the rectangular prism

Count the number of cubes along the length ($l = 3$), width ($w = 3$), and height ($h = 5$). The total number of small cubes $n=l\times w\times h=3\times3\times5 = 45$.

Step3: Calculate the volume of the rectangular prism

The volume of the rectangular prism $V=n\times V_{cube}$. Substitute $n = 45$ and $V_{cube}=\frac{1}{27}$ into the formula: $V = 45\times\frac{1}{27}=\frac{45}{27}=\frac{5}{3}=1\frac{2}{3}$ $ft^3$.

Another way:

Step1: Calculate the dimensions of the rectangular prism

Length of the rectangular prism $l=3\times\frac{1}{3}=1$ ft, width $w = 3\times\frac{1}{3}=1$ ft, height $h=5\times\frac{1}{3}=\frac{5}{3}$ ft.

Step2: Use the formula for the volume of a rectangular prism

The formula for the volume of a rectangular prism is $V=l\times w\times h$. Substitute $l = 1$, $w = 1$, and $h=\frac{5}{3}$ into the formula: $V=1\times1\times\frac{5}{3}=\frac{5}{3}=1\frac{2}{3}$ $ft^3$.

Answer:

$1\frac{2}{3}$ $ft^3$