Question

find the volume of the cube. 1\frac{1}{3} mi. 1\frac{1}{3} mi. 1\frac{1}{3} mi. write your answer as a whole number, a proper fraction, or a mixed number. cubic miles

Explanation:

Step1: Convert mixed - number to improper fraction

$1\frac{1}{3}=\frac{1\times3 + 1}{3}=\frac{4}{3}$

Step2: Use volume formula for cube

The volume $V$ of a cube with side length $s$ is $V=s^3$. Here $s = \frac{4}{3}$, so $V=(\frac{4}{3})^3$.

Step3: Calculate the cube of the fraction

$(\frac{4}{3})^3=\frac{4^3}{3^3}=\frac{64}{27}$

Step4: Convert to mixed - number

$\frac{64}{27}=2\frac{10}{27}$

Answer:

$2\frac{10}{27}$