What is the volume of a box that can fit 27 number cubes, each with an edge length of (2/3) inch?

What is the volume of a box that can fit 27 number cubes, each with an edge length of (2/3) inch?

• A. 6 cubic inches
• B. 8 cubic inches
• C. 10 cubic inches
• D. 12 cubic inches

Answer: (B)

To determine the volume of the box that can fit 27 number cubes, we first need to find the volume of one individual cube. Each cube has an edge length of (2/3) inch. The formula for the volume of a cube is given by the side length cubed: \[ \text{Volume of one cube} = \left(\frac{2}{3}\right)^3 \] Calculating this: \[ \left(\frac{2}{3}\right)^3 = \frac{2^3}{3^3} = \frac{8}{27} \text{ cubic inches} \] Next, since there are 27 of these cubes, the total volume occupied by all the cubes can be calculated by multiplying the volume of one cube by the number of cubes: \[ \text{Total volume} = 27 \times \frac{8}{27} \] When we perform this multiplication, the \(27\) cancels out: \[ \text{Total volume} = 8 \text{ cubic inches} \] Thus, the volume of the box that can fit all 27 number cubes is 8 cubic inches. This aligns perfectly with the correct answer.

To determine the volume of the box that can fit 27 number cubes, we first need to find the volume of one individual cube. Each cube has an edge length of (2/3) inch. The formula for the volume of a cube is given by the side length cubed:

[

\text{Volume of one cube} = \left(\frac{2}{3}\right)^3

]

Calculating this:

[

\left(\frac{2}{3}\right)^3 = \frac{2^3}{3^3} = \frac{8}{27} \text{ cubic inches}

]

Next, since there are 27 of these cubes, the total volume occupied by all the cubes can be calculated by multiplying the volume of one cube by the number of cubes:

[

\text{Total volume} = 27 \times \frac{8}{27}

]

When we perform this multiplication, the (27) cancels out:

[

\text{Total volume} = 8 \text{ cubic inches}

]

Thus, the volume of the box that can fit all 27 number cubes is 8 cubic inches. This aligns perfectly with the correct answer.