Question

how many blocks with dimensions of 1/3×1×1 can fit in a unit cube? 2 3 6 9

Explanation:

Step1: Calculate the volume of the small block

The volume formula for a rectangular prism is \(V = l\times w\times h\). For the small block with dimensions \(\frac{1}{3}\times1\times1\), its volume \(V_{small}=\frac{1}{3}\times1\times1=\frac{1}{3}\)

Step2: Calculate the volume of the unit - cube

The volume formula for a cube is \(V = s^{3}\), where \(s = 1\) (since it's a unit - cube). So \(V_{unit - cube}=1\times1\times1 = 1\)

Step3: Find the number of small blocks that fit

Let \(n\) be the number of small blocks. We use the formula \(n=\frac{V_{unit - cube}}{V_{small}}\). Substitute \(V_{unit - cube}=1\) and \(V_{small}=\frac{1}{3}\) into the formula: \(n=\frac{1}{\frac{1}{3}}=1\times3 = 3\)

Answer:

3