Question

how many blocks with dimensions of \\( \frac{1}{3} \times 1 \times 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 block with dimensions \(\frac{1}{3}\times1\times1\), its volume \(V_{block}=\frac{1}{3}\times1\times1=\frac{1}{3}\)

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 \(V_{cube}=1\times1\times1 = 1\)

Step3: Find the number of blocks

To find the number of blocks \(n\) that can fit into the cube, use the formula \(n=\frac{V_{cube}}{V_{block}}\). Substitute \(V_{cube}=1\) and \(V_{block}=\frac{1}{3}\) into the formula: \(n=\frac{1}{\frac{1}{3}}=1\times3 = 3\)

Answer:

3