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To calculate the density of the sand, we need its mass and its volume.

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Answer

0.625 g/cm30.625 \text{ g/cm}^3

Step-by-step solution

5 steps

Here's the solution to 9(a):

  1. (a) To calculate the density of the sand, we need its mass and its volume.

  1. Determine the mass of the water that fills the bottle.

    Mass of water = (Mass of bottle + water) - (Mass of empty bottle)
    Mass of water = 98 g−35 g=63 g98 \text{ g} - 35 \text{ g} = 63 \text{ g}

  2. Determine the volume of the bottle.

    Assuming the density of water is 1 g/cm31 \text{ g/cm}^3.
    Volume of bottle = Volume of water that fills the bottle

    Vbottle=Mass of waterDensity of water=63 g1 g/cm3=63 cm3V_{bottle} = \frac{\text{Mass of water}}{\text{Density of water}} = \frac{63 \text{ g}}{1 \text{ g/cm}^3} = 63 \text{ cm}^3

  3. Determine the mass of the sand.

    Mass of sand = (Mass of bottle + some sand) - (Mass of empty bottle)
    Mass of sand = 65 g−35 g=30 g65 \text{ g} - 35 \text{ g} = 30 \text{ g}

  4. Determine the volume of the sand.

    The line "Mass of bottle + sand + water on top of the sand = 80g" tells us the total mass when the bottle is filled with sand and then water is added to fill the remaining space.
    Mass of (sand + water) in the bottle = (Mass of bottle + sand + water) - (Mass of empty bottle)
    Mass of (sand + water) = 80 g−35 g=45 g80 \text{ g} - 35 \text{ g} = 45 \text{ g}

    Now, subtract the mass of the sand (from Step 3) to find the mass of the water added on top of the sand.
    Mass of water added = Mass of (sand + water) - Mass of sand
    Mass of water added = 45 g−30 g=15 g45 \text{ g} - 30 \text{ g} = 15 \text{ g}

    Using the density of water (1 g/cm31 \text{ g/cm}^3), find the volume of the water added.
    Volume of water added = Mass of water addedDensity of water=15 g1 g/cm3=15 cm3\frac{\text{Mass of water added}}{\text{Density of water}} = \frac{15 \text{ g}}{1 \text{ g/cm}^3} = 15 \text{ cm}^3

    The volume of the sand is the total volume of the bottle minus the volume of the water added.
    Volume of sand = Volume of bottle - Volume of water added
    Volume of sand = 63 cm3−15 cm3=48 cm363 \text{ cm}^3 - 15 \text{ cm}^3 = 48 \text{ cm}^3

  5. Calculate the density of the sand.

    Density of sand = Mass of sandVolume of sand\frac{\text{Mass of sand}}{\text{Volume of sand}}

    Density of sand=30 g48 cm3\text{Density of sand} = \frac{30 \text{ g}}{48 \text{ cm}^3} Density of sand=58 g/cm3\text{Density of sand} = \frac{5}{8} \text{ g/cm}^3 Density of sand=0.625 g/cm3\text{Density of sand} = 0.625 \text{ g/cm}^3

    The density of the sand is 0.625 g/cm30.625 \text{ g/cm}^3.

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