Which will occupy more space- 720 g of mahogany wood (of density 0.720 `"g/cm"^3`) or 2710 g of marble (of density 2.71 `"g/cm"^3`) ?

Answer

To determine which material occupies more space, we will calculate the volume occupied by both 720 g of mahogany wood and 2710 g of marble using the formula that relates mass, density, and volume.

### Step-by-Step Solution:

**Step 1: Understand the relationship between mass, density, and volume.**
The formula that relates these quantities is:
\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]
From this, we can rearrange the formula to find volume:
\[ \text{Volume} = \frac{\text{Mass}}{\text{Density}} \]

**Step 2: Calculate the volume of mahogany wood.**
Given:
- Mass of mahogany wood (M1) = 720 g
- Density of mahogany wood (D1) = 0.720 g/cm³

Using the formula:
\[ V1 = \frac{M1}{D1} = \frac{720 \, \text{g}}{0.720 \, \text{g/cm}^3} \]

Calculating:
\[ V1 = \frac{720}{0.720} = 1000 \, \text{cm}^3 \]

**Step 3: Calculate the volume of marble.**
Given:
- Mass of marble (M2) = 2710 g
- Density of marble (D2) = 2.71 g/cm³

Using the formula:
\[ V2 = \frac{M2}{D2} = \frac{2710 \, \text{g}}{2.71 \, \text{g/cm}^3} \]

Calculating:
\[ V2 = \frac{2710}{2.71} = 1000 \, \text{cm}^3 \]

**Step 4: Compare the volumes.**
From the calculations:
- Volume of mahogany wood (V1) = 1000 cm³
- Volume of marble (V2) = 1000 cm³

Both volumes are equal.

### Conclusion:
Both 720 g of mahogany wood and 2710 g of marble occupy the same volume of 1000 cm³.

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