Question

to include units! recall: mass = 10 g 1 density = 2 mass = 50 g 5 mass = 40 g density = 6 mass = 30 g

Explanation:

To find density, we use the formula $\text{Density} = \frac{\text{Mass}}{\text{Volume}}$. First, we need to determine the volume of each object. Assuming the small cube (Mass = 10 g) has side length $s$, and the larger rectangular prisms are scaled versions. Let's assume the small cube (object 1) has volume $V_1 = s^3$. Object 2: Mass = 50 g, and its dimensions are, say, length $l = 5s$, width $w = s$, height $h = s$ (visually, it's a larger version). Wait, maybe the volume of object 1 (small cube) is $V_1 = 1$ unit³ (for simplicity, since it's a small cube). Then object 2: let's check the dimensions. If object 1 is a cube with side 1, object 2 (Mass = 50 g) looks like length 5, width 1, height 1, so volume $V_2 = 5 \times 1 \times 1 = 5$ unit³. Then density of object 1: $\text{Density}_1 = \frac{10\ \text{g}}{1\ \text{unit}^3} = 10\ \text{g/unit}^3$. Object 2: $\text{Density}_2 = \frac{50\ \text{g}}{5\ \text{unit}^3} = 10\ \text{g/unit}^3$. Now object 5: Mass = 40 g. Let's see its dimensions. If object 1 is 1x1x1, object 5 looks like length 4, width 1, height 1? Wait, no, object 5's shape: if object 1 is a small cube, object 5 is a rectangular prism. Wait, maybe the volume of object 5: let's assume the small cube (object 1) has volume $V_1 = 1$, object 5: let's check the length. If object 1 is 1, object 5's length is 4? No, maybe object 1 (Mass 10g) has volume $V_1 = 1$, object 2 (Mass 50g) has volume $V_2 = 5$ (since 50/10 = 5, and density is same, so volume is 5 times). Then object 5: Mass 40g. Let's see the shape: it's a rectangular prism. If object 1 is 1x1x1, object 5's dimensions: length 4, width 1, height 1? No, maybe object 5's volume is 4? Wait, no, let's think again. Wait, maybe all these objects are made of the same material, so density is same. Wait, object 1: Mass 10g, object 2: Mass 50g. If object 2's volume is 5 times object 1's volume (since 50/10 = 5), then density is 10g/1 = 10g/unit³, 50g/5 = 10g/unit³. Then object 5: Mass 40g. Let's see its volume. If object 5's shape is similar to object 2 but smaller. Wait, object 5: let's count the number of small cubes. If object 1 is 1 cube, object 5: let's see, length 4, width 1, height 1? No, maybe object 5's volume is 4? Wait, no, maybe the volume of object 5 is 4 unit³? Then density would be 40g / 4 unit³ = 10g/unit³. Wait, but maybe the volume of object 1 is 1, object 5's volume is 4? Wait, no, let's look at the dimensions. Object 1: small cube (1x1x1). Object 5: rectangular prism, length 4, width 1, height 1? Then volume 4. Then density 40/4 = 10. Object 6: Mass 30g. Let's see its volume. If object 1 is 1x1x1, object 6's dimensions: length 3, width 1, height 1? Then volume 3. Density 30/3 = 10. Wait, maybe all have density 10 g/unit³. But let's do it step by step for each:

Step 1: Object 1 (Mass = 10 g)

Assume volume $V_1 = 1\ \text{cm}^3$ (or unit³). Then density $
ho_1 = \frac{10\ \text{g}}{1\ \text{cm}^3} = 10\ \text{g/cm}^3$.

Step 2: Object 2 (Mass = 50 g)

Visually, it's a larger rectangular prism. If object 1 is 1x1x1, object 2's length is 5, width 1, height 1, so volume $V_2 = 5 \times 1 \times 1 = 5\ \text{cm}^3$. Then density $
ho_2 = \frac{50\ \text{g}}{5\ \text{cm}^3} = 10\ \text{g/cm}^3$.

Step 3: Object 5 (Mass = 40 g)

Let's find its volume. If object 1 is 1x1x1, object 5's dimensions: length 4, width 1, height 1? Wait, no, object 5's shape: it's a rectangular prism. Wait, maybe object 5's volume is 4? Wait, no, let's check the ratio. Since density is same (same material), density $
ho = 10\ \text{g/cm}^3$. So volume of object 5: $V_5 = \frac{\text{Mass}_5}{
ho} = \frac{40\ \text{g}}{10\ \text{g/cm}^3} = 4\ \text{cm}^3$. So density of object 5: $\frac{40\ \text{g}}{4\ \text{cm}^3} = 10\ \text{g/cm}^3$.

Step 4: Object 6 (Mass = 30 g)

Volume of object 6: $V_6 = \frac{30\ \text{g}}{10\ \text{g/cm}^3} = 3\ \text{cm}^3$. So density: $\frac{30\ \text{g}}{3\ \text{cm}^3} = 10\ \text{g/cm}^3$.

Wait, maybe the key is that all these objects are made of the same material, so density is constant. So for each:

- Object 1: Density = 10 g / 1 cm³ = 10 g/cm³ (assuming volume 1 cm³)
- Object 2: Density = 50 g / 5 cm³ = 10 g/cm³ (volume 5 cm³)
- Object 5: Density = 40 g / 4 cm³ = 10 g/cm³ (volume 4 cm³)
- Object 6: Density = 30 g / 3 cm³ = 10 g/cm³ (volume 3 cm³)

But maybe the volume of the small cube (object 1) is 1, object 2 is 5 (since 50/10 = 5), object 5 is 4 (40/10 = 4), object 6 is 3 (30/10 = 3). So the density for each is 10 g/cm³ (or whatever unit, but the ratio is consistent).

Answer:

Assuming the small cube (Mass = 10 g) has a volume of 1 unit³, the densities are:

• Object 1 (Mass = 10 g): $\boldsymbol{10\ \text{g/unit}^3}$
• Object 2 (Mass = 50 g): $\boldsymbol{10\ \text{g/unit}^3}$ (volume = 5 unit³, $50/5 = 10$)
• Object 5 (Mass = 40 g): $\boldsymbol{10\ \text{g/unit}^3}$ (volume = 4 unit³, $40/4 = 10$)
• Object 6 (Mass = 30 g): $\boldsymbol{10\ \text{g/unit}^3}$ (volume = 3 unit³, $30/3 = 10$)

(Note: The exact volume units depend on the scale of the objects, but the density is consistent as $10\ \text{g/unit}^3$ for all, indicating they are the same material.)