Grain Volume Calculation

The question asks us to determine which of the given grains will occupy the largest volume when we have 1 kg of each. We are provided with single-grain density and bulk density for four types of grains: Rice, Wheat, Millet, and Maize.

When dealing with a quantity of grain in bulk, like 1 kg which consists of many individual grains, the volume it occupies includes the spaces between the grains. Therefore, the relevant density to use for calculating the volume of a given mass of grain is the bulk density.

The relationship between mass, volume, and density is given by the formula:

\begin{equation} \text{Volume} = \frac{\text{Mass}}{\text{Density}} \quad \text{or} \quad V = \frac{m}{\rho} \end{equation}

We are given the mass $m = 1$ kg. We need to convert this to grams since the densities are given in g/cm$^3$.

\begin{equation} 1 \text{ kg} = 1000 \text{ g} \end{equation}

We will use the bulk density ($\rho_{bulk}$) from the table for each grain to calculate its volume.

Calculating Volume for Each Grain

Let's calculate the volume for 1000 g of each grain using its bulk density:

• Rice:
• Mass $m = 1000$ g
• Bulk density $\rho_{Rice} = 0.56$ g/cm$^3$
• Volume $V_{Rice} = \frac{1000 \text{ g}}{0.56 \text{ g/cm}^3} \approx 1785.71$ cm$^3$

• Wheat:
• Mass $m = 1000$ g
• Bulk density $\rho_{Wheat} = 0.80$ g/cm$^3$
• Volume $V_{Wheat} = \frac{1000 \text{ g}}{0.80 \text{ g/cm}^3} = 1250$ cm$^3$

• Millet:
• Mass $m = 1000$ g
• Bulk density $\rho_{Millet} = 0.77$ g/cm$^3$
• Volume $V_{Millet} = \frac{1000 \text{ g}}{0.77 \text{ g/cm}^3} \approx 1298.70$ cm$^3$

• Maize:
• Mass $m = 1000$ g
• Bulk density $\rho_{Maize} = 0.68$ g/cm$^3$
• Volume $V_{Maize} = \frac{1000 \text{ g}}{0.68 \text{ g/cm}^3} \approx 1470.59$ cm$^3$

Comparing the Volumes

Now, let's compare the calculated volumes for each grain:

• Rice: $\approx 1785.71$ cm$^3$
• Wheat: $1250$ cm$^3$
• Millet: $\approx 1298.70$ cm$^3$
• Maize: $\approx 1470.59$ cm$^3$

By comparing these values, we can see that Rice has the largest volume among the four grains for a mass of 1 kg.

The grain with the largest volume is Rice.