Question

a diagram of a cube is shown above. what is the volume, in cubic inches, of the cube? show your thinking 1\frac{7}{8} 7\frac{1}{2} 15\frac{5}{8} 20\frac{5}{6}

Explanation:

Step1: Convert side - length to improper fraction

The side - length of the cube is $2\frac{1}{2}$ inches. Convert it to an improper fraction: $2\frac{1}{2}=\frac{2\times2 + 1}{2}=\frac{5}{2}$ inches.

Step2: Apply volume formula for a cube

The volume formula of a cube is $V = s^3$, where $s$ is the side - length. Substitute $s=\frac{5}{2}$ into the formula: $V=(\frac{5}{2})^3=\frac{5}{2}\times\frac{5}{2}\times\frac{5}{2}$.

Step3: Calculate the product

$\frac{5}{2}\times\frac{5}{2}\times\frac{5}{2}=\frac{5\times5\times5}{2\times2\times2}=\frac{125}{8}=15\frac{5}{8}$ cubic inches.

Answer:

$15\frac{5}{8}$