3.1.2 Measuring Density

• Density is defined as mass per unit volume
• What is the formula for density?

  \rho = \frac{m}{V}</latex>
• Density is typically measured in kilograms per cubic meter (kg/m³) or grams per cubic centimeter (g/cm³).
• If a rock has a mass of 1000 kg and a volume of 0.5 m³, its density is 2000 kg/m³
• The density of air at standard temperature and pressure (STP) is 1.225 kg/m³.
• Density is typically measured in kilograms per cubic meter (kg/m³) or grams per cubic centimeter
• What does density measure?

  Mass per unit volume
• Common units for density are kg/m³ or g/cm³.
• Common units for density are kilograms per cubic meter (kg/m³) or grams per cubic centimeter
• Steps to measure mass using a balance

  1️⃣ Calibrate the balance

  2️⃣ Place the object on the weighing platform

  3️⃣ Read the measurement

  4️⃣ Record the mass with appropriate units
• The formula for density requires accurate mass measurements
• What is the first step in measuring mass using a balance?

  Calibrate the balance
• The formula for density, $\rho =$$\frac{m}{V}$, requires accurate mass measurements
• Calibrating the balance is the first step in measuring mass.
• Match the shape with its volume formula:

  Cube ↔️ V = a^{3}</latex>

  Cylinder ↔️ $V =$$\pi r^{2} h$

  Sphere ↔️ $V =$$\frac{4}{3} \pi r^{3}$
• The volume of a cube is calculated using the formula $V =$$a^{3}$, where $a$ is the length of one side
• Steps to measure the volume of regular shapes:

  1️⃣ Measure the required dimensions accurately

  2️⃣ Substitute the measured values into the appropriate formula

  3️⃣ Calculate the volume using the formula

  4️⃣ Record the volume with the correct units
• What is the volume of a cube with sides measuring 5 cm?

  125 cm³
• What method is used to measure the volume of irregular shapes?

  Displacement method
• Steps to measure the volume of irregular shapes using the displacement method:

  1️⃣ Fill the graduated cylinder with water to a known volume ($V_{1}$)

  2️⃣ Carefully immerse the irregular object into the water

  3️⃣ Observe the new volume ($V_{2}$)

  4️⃣ Calculate the volume of the object using the formula: $V =$$V_{2} - V_{1}$
• The formula for calculating the volume of an irregular object using the displacement method is $V =$$V_{2} - V_{1}$, where $V_{1}$ is the initial volume
• Density is defined as mass per unit volume.
• What is the formula for density?

  $\rho =$$\frac{m}{V}$
• Density is typically measured in kilograms per cubic meter ($kg / m^{3}$) or grams per cubic centimeter
• What is the density of a rock with a mass of 1000 kg and a volume of 0.5 m³?

  2000 kg/m³
• Density measures the amount of mass per unit volume.
• Density is measured in units such as kilograms per cubic meter or grams per cubic centimeter
• What is used to measure the volume of regular shapes like cubes, cylinders, and spheres?

  Specific formulas
• The volume of a cube is calculated using the formula V = a^{3}
• What measurements are needed to calculate the volume of a cylinder?

  Radius and height
• The volume of a sphere depends only on its radius.
• To measure the volume of cubes, cylinders, and spheres, specific formulas
• What is the formula for the volume of a cube with side length $a$?


  $V =$$a^{3}$
• Match the shape with its volume formula:

  Cube ↔️ $V =$$a^{3}$

  Cylinder ↔️ $V =$$\pi r^{2} h$

  Sphere ↔️ $V =$$\frac{4}{3} \pi r^{3}$
• Steps to measure the volume of regular shapes

  1️⃣ Measure the required dimensions

  2️⃣ Substitute into the formula

  3️⃣ Calculate the volume

  4️⃣ Record with correct units
• What is the formula for the volume of a cylinder with radius $r$ and height $h$?


  $V =$$\pi r^{2} h$
• The height of a cylinder is needed to calculate its volume.
• What is the formula for the volume of a sphere with radius $r$?


  V = \frac{4}{3} \pi r^{3}</latex>
• To measure the volume of cubes, cylinders, and spheres, specific formulas
• Steps to measure the volume of regular shapes

  1️⃣ Measure the required dimensions

  2️⃣ Substitute into the formula

  3️⃣ Calculate the volume

  4️⃣ Record with correct units