Question

1. exploration

a sugar cube has a volume of about 1 cubic centimeter. about how large of a box would you need to hold 1,000,000 sugar cubes?

Explanation:

Step1: Recall volume formula for box

The volume of a box (rectangular - prism) is \(V = l\times w\times h\). We want to find the volume of a box that can hold 1,000,000 sugar - cubes, and each sugar - cube has a volume of \(V_{cube}=1\ cm^{3}\).

Step2: Calculate total volume

The total volume \(V\) of the box needed to hold \(n = 1000000\) sugar - cubes is \(V=n\times V_{cube}\). Since \(n = 1000000\) and \(V_{cube}=1\ cm^{3}\), then \(V=1000000\times1\ cm^{3}=1000000\ cm^{3}\).

Step3: Convert to larger unit

We know that \(1\ dm^{3}=1000\ cm^{3}\) and \(1\ m^{3}=1000\ dm^{3}\). To convert \(1000000\ cm^{3}\) to \(dm^{3}\), we use the conversion factor \(\frac{1\ dm^{3}}{1000\ cm^{3}}\). So \(V=\frac{1000000\ cm^{3}}{1000\ cm^{3}/dm^{3}} = 1000\ dm^{3}\), and to convert to \(m^{3}\), we use the conversion factor \(\frac{1\ m^{3}}{1000\ dm^{3}}\), so \(V = 1\ m^{3}\).

Answer:

The box would need to have a volume of 1 cubic meter (or 1,000,000 cubic centimeters or 1000 cubic decimeters) to hold 1,000,000 sugar - cubes.