Physics Chapter on Volume and Density

Volume

• Volume is the amount of space an object occupies.
• The SI unit of volume is cubic meter (m³).
• 1 m³ = 10⁶ cm³.
• 1 m³ = 10³ dm³.

Density

• Density is the mass per unit volume of a substance.
• The SI unit of density is kg/m³.
• Relative density is the ratio of the density of a substance to the density of water.
• Water has a maximum density at 4°C.

Area

• Area is the amount of surface covered by a two-dimensional figure.
• The SI unit of area is square meter (m²).
• The area of a closed figure can be measured using graph paper.
• Formulae for calculating the areas of regular shapes:
  • Square: (side)²
  • Rectangle: length x breadth
  • Circle: π x (radius)²
  • Triangle: 1/2 x base x height

Speed

• Speed is the distance traveled per unit time.
• The SI unit of speed is meter per second (m/s).
• Speed can be measured with a speedometer.
• Distance can be measured with an odometer.
• Distance = Speed x Time.
• For equal distances, lower travel time means higher speed.
• For equal time intervals, greater distance traveled means higher speed.

Volume

• The space occupied by an object is its volume.
• The SI unit of volume is cubic meter (m3).
• One cubic meter is the volume of a cube with each side 1 meter long.
• Smaller units of volume are cubic centimeter (cm3), cubic decimeter (dm3).
• 1 m3 = 106 cm3
• 1 m3 = 103 dm3

Density

• Density is mass per unit volume of a substance.
• The SI unit of density is kg m-3, and its C.G.S. unit is g cm-3.
• 1 g cm-3 = 1000 kg m-3.
• Relative density = Density of the substance / Density of water.
• The volume of an irregular solid can be measured using a measuring cylinder by the method of displacement of liquid.

Area

• The amount of flat surface or region occupied by a closed figure is called area.
• The SI unit of area is square meter (m2).
• To measure the area of an irregular lamina using a graph paper, place the lamina over a graph paper, draw its boundary line, and count the number of complete squares, half squares, and more than half squares within the boundary line.

Speed

• Speed is the distance traveled by a body in a unit of time.
• The SI unit of speed is meter per second (m s-1).
• Speed is measured by a speedometer.
• Distance covered = Speed × Time.
• If speed is the same throughout a journey, then the motion is uniform.
• If speed varies, then the motion is non-uniform.
• For equal distance, less travel time means higher speed.
• For equal time interval, greater distance covered means higher speed.

Temperature and Density

• When temperature increases in the case of a gas or liquid, their volume increases, so the density decreases.
• When temperature increases in the case of a solid, the volume does not change much, so the density is not altered much.
• The density of water at 4°C is 1 g cm-3 or 1000 kg m-3.
• Water when heated from 0°C to 4°C, it contracts so the density of water increases and becomes maximum at 4°C.
• When water is heated from 4°C to 10°C, it expands, so density decreases.

Volume

• Volume is the space occupied by an object
• The S.I. unit of volume is cubic meter (m³)
• 1 cubic meter is the volume of a cube with each side 1 meter long
• 1 m³ = 10⁶ cm³
• 1 m³ = 10³ dm³

Measuring Volume

• The volume of an irregular solid can be measured by the water displacement method using a measuring cylinder.
• Fill the cylinder partially with water
• Note the initial water level (V1)
• Immerse the irregular solid completely in the water
• Note the new water level (V2)
• The difference between the two water levels (V2-V1) gives the volume of the irregular solid

Area

• Area is the amount of flat surface or region occupied by a closed figure.
• To measure the area of an irregular closed figure using graph paper:
  • Place the closed figure on the graph paper
  • Outline the figure
  • Count the number of full, half, and more than half squares enclosed by the figure
  • Ignore squares that are less than half enclosed
  • Calculate the area:
    • Full squares = 1 square unit each
    • Half squares = 1/2 square unit each
    • More than half squares = 1 square unit each

Formulae for Measuring Area

• Area of a square = (side)²
• Area of a rectangle = length × breadth
• Area of a circle = π × (radius)²
• Surface area of a cylinder = 2π × (radius) × length
• Surface area of a sphere = 4π × (radius)²
• Area of a triangle = 1/2 × base × height

Density

• Density is the mass per unit volume of a substance
• The S.I. unit of density is kg m^-3
• The C.G.S. unit of density is g cm^-3
• 1 g cm^-3 = 1000 kg m^-3
• The density of water at 4°C is 1 g cm^-3 or 1000 kg m^-3

Variation in Density

• When temperature increases in solids, the volume does not change much, so the density is not altered much
• When temperature increases in gases and liquids, the volume does not change much, so the density is not altered much

Speed

• Speed is the distance travelled by a body in unit time.
• It tells us how fast or slow a body is moving.
• The S.I. unit of speed is meter per second (m s^-1)

Types of Motion

• Uniform motion: When speed is the same throughout a journey
• Non-uniform motion: When speed varies

Measuring Speed and Distance

• Speed is measured by a speedometer
• Distance moved by a vehicle is measured by an odometer

Speed Calculations

• Distance covered = Speed × Time
• For equal distance, less travel time means higher speed
• For equal time interval, greater distance covered means higher speed

Volume

• Volume is the amount of space an object occupies.
• The SI unit of volume is cubic meter (m³).
• One cubic meter is the volume of a cube with each side measuring 1 meter.

Density

• Density is the mass per unit volume of a substance.
• Units of density are g/cm³ or kg/m³.
• Relative density is the ratio of the density of a substance to the density of water.

Temperature and Density

• In solids, density changes very little with temperature changes.
• In gases and liquids, density changes slightly with temperature changes.

Area

• Area is the amount of flat surface or region occupied by a closed figure.
• Area can be measured using graph paper by counting full, half, and more-than-half squares.

Calculating Area of Regular Shapes

• Area of a square = (side)²
• Area of a rectangle = length × breadth
• Area of a circle = π × (radius)²
• Surface area of a cylinder = 2π × (radius) × length
• Surface area of a sphere = 4π × (radius)²
• Area of a triangle = ½ × base × height

Speed

• Speed is the distance traveled by a body in unit time.
• The SI unit of speed is meters per second (m/s).
• Speed is measured by a speedometer.
• Distance covered = Speed × Time.

Uniform and Non-Uniform Motion

• If speed remains constant throughout a journey, it is called uniform motion.
• If speed varies during a journey, it is called non-uniform motion.

Measuring Volume

• Two smaller units of volume are cubic centimeter (cm³) and cubic decimeter (dm³).
• 1 m³ = 10⁶ cm³
• 1 m³ = 10³ dm³
• The volume of a cuboid is calculated by multiplying length, breadth, and height.
• The volume of an irregular solid can be measured by the displacement of liquid method.

Measuring Area of Irregular Shapes

• Place the irregular object on graph paper.
• Draw its boundary line on the graph paper.
• Count the number of complete squares, half squares, and more-than-half squares within the boundary line.
• Ignore squares that are less than half.
• The sum of the areas of complete and incomplete squares gives the approximate area.

Density of Water

• The density of water at 4°C is 1 g/cm³ or 1000 kg/m³.
• Water contracts when heated from 0°C to 4°C, increasing its density to a maximum at 4°C.
• Water expands when heated from 4°C to 10°C, decreasing its density.

Volume

• Volume is the space occupied by an object.
• The SI unit of volume is cubic meter (m3).
• One cubic meter is the volume of a cube with each side 1 meter long.
• 1 m3 = 106 cm3
• 1 m3 = 103 dm3

Density

• Density is mass per unit volume of a substance.
• The unit of density is g/cm3 or kg/m3.
• Relative density = Density of the substance/Density of the water
• The density of water at 4°C is 1 g cm-3 or 1000 kg m-3
• The density of a substance is defined as the mass of a unit volume of that substance.
• The SI unit of density is kg m-3 and its C.G.S. unit is g cm-3.
• 1 g cm-3 = 1000 kg m-3

Area

• Area is the amount of flat surface or region occupied by a closed figure.
• The SI unit of area is square meter (m2).

Measuring Area of an Irregular Figure using Graph Paper

• Place the closed figure on a squared paper where every square measures 1 cm × 1 cm.
• Make an outline of the figure.
• Count the number of squares enclosed by the figure:
  • Full squares
  • Half squares
  • More than half squares
  • Ignore portions of the area that are less than half a square.

Measuring Volume of an Irregular Solid

• Use a measuring cylinder.
• Fill it partially with water and note the reading (V1).
• Tie the irregular solid with a thread and dip it completely into the water.
• Note the new water level reading (V2).
• The volume of the irregular solid is (V2 - V1).

Formulas for Measuring Area

• Area of square = (side)2
• Area of rectangle = length × breadth
• Area of circle = π×(radius)2
• Surface area of cylinder = 2π×(radius)×length
• Surface area of sphere = 4π×(radius)2
• Area of triangle = 1/2×base×height

Measuring Volume

• Volume of a cuboid = length x breadth x height

Speed

• The speed of a body is the distance traveled by the body in unit time.
• The S.I. unit of speed is meter per second (m s-1).

Types of Motions

• Uniform motion: If speed is the same throughout a journey, then the motion is uniform.
• Non-uniform motion: If speed varies, then the motion is non-uniform.

Measuring Speed and Distance

• Speed is measured by a speedometer.
• Distance moved by a vehicle is measured by an odometer.

Volume

• The space occupied by an object is its volume.
• The standard unit of volume is the cubic meter (m3).
• One cubic meter is the volume of a cube with sides of 1 meter each.
• Smaller units of volume include cubic centimeters (cm3) and cubic decimeters (dm3).
• 1 m3 = 106 cm3
• 1 m3 = 103 dm3

Density

• Density is defined as the mass per unit volume of a substance.
• The standard unit of density is kilograms per cubic meter (kg/m3).
• The CGS unit of density is grams per cubic centimeter (g/cm3).
• 1 g cm-3 = 1000 kg m-3
• Density can vary with temperature, especially for gases and liquids.

Measuring Volume

• The volume of a cuboid is calculated by multiplying its length, breadth, and height.
• The volume of an irregular solid can be measured by the displacement method using a measuring cylinder.

Measuring Area

• The area of a closed figure is the amount of flat surface it occupies.
• To measure the area of a closed figure using graph paper:
  • Place the figure on the graph paper.
  • Outline the figure.
  • Count the number of complete squares, half squares, and squares more than half.
  • The area is calculated by assuming:
    • Each full square is 1 square unit.
    • Portions less than half a square are ignored.
    • Portions more than half a square are counted as one square unit.
    • Exactly half squares are counted as one square unit.

Area Formulas

• Area of a square = (side)2
• Area of a rectangle = length × breadth
• Area of a circle = π × (radius)2
• Surface area of a cylinder = 2π × (radius) × length
• Surface area of a sphere = 4π × (radius)2
• Area of a triangle = 1/2 × base × height

Speed

• Speed is the distance traveled by a body in unit time.
• It describes how fast or slow a body is moving.
• The standard unit of speed is meters per second (m/s).
• A speedometer measures speed, and an odometer measures distance traveled.
• Distance covered = Speed × Time
• For a fixed distance, less travel time means higher speed.
• For equal time intervals, a greater distance covered means higher speed.

Types of Motion

• Uniform motion: Speed is constant throughout the journey.
• Non-uniform motion: Speed varies throughout the journey.

Water Density

• The density of water is highest at 4°C.
• Water contracts from 0°C to 4°C, increasing its density.
• Water expands from 4°C to 10°C, decreasing its density.
• The density of water at 4°C is 1 g cm-3 or 1000 kg m-3.

Volume

• The space occupied by an object is called its volume.
• The standard unit of volume is cubic meter (m3).
• It is the volume of a cube with each side equal to 1 meter long.
• Smaller units of volume include cubic centimeter (cm3) and cubic decimeter (dm3).
• 1 m3 = 106 cm3
• 1 m3 = 103 dm3

Density

• It is the mass per unit volume of a substance.
• It is typically measured in grams per cubic centimeter (g/cm3) or kilograms per cubic meter (kg/m3).
• The relative density of a substance is the ratio of its density to the density of water.
• The density of water at 4°C is 1 g cm-3 or 1000 kg m-3.
• The density of solids, liquids, and gases can vary with temperature.
  • When temperature increases in solids, the volume changes slightly, so the density is not significantly altered.
  • When temperature increases in liquids and gases, the volume changes, which can affect the density.

Area

• The amount of flat surface or region occupied by a closed figure is called its area.
• To measure the area of a closed figure using graph paper, follow these steps:
  • Place the figure on the graph paper.
  • Outline the figure.
  • Count the squares enclosed by the figure.
  • Calculate the area by considering complete squares, half squares, and more than half squares.
• Formulas for measuring the area of regular bodies include:
  • Area of a square = (side)2
  • Area of a rectangle = length × breadth
  • Area of a circle = π×(radius)2
  • Surface area of a cylinder = 2π×(radius)× length
  • Surface area of a sphere = 4π×(radius)2
  • Area of a triangle =12×base×height

Speed

• Speed of a body is the distance traveled by the body in unit time.
• It tells us how fast or slow an object is moving.
• Speed is measured in meters per second (m s-1).
• Uniform motion occurs when speed is constant during a journey.
• Non-uniform motion occurs when speed varies during a journey.
• Speedometers measure speed.
• Odometers measure distance.
• Distance covered = Speed × Time
• For equal distances, a shorter travel time means a higher speed.
• For an equal time interval, a longer distance traveled means a higher speed.

Measuring Volume of Irregular Solids

• The volume of a cuboid can be measured by multiplying its length, breadth, and height.
• The volume of an irregular solid can be measured using a measuring cylinder by water displacement.
  • Partially fill the cylinder with water, note the water level (V1).
  • Submerge the solid completely in the water, note the new water level (V2).
  • The volume of the solid is the difference between the two water levels (V2 - V1).

Measuring Area of Irregular Lamina

• Place the lamina on a graph paper.
• Trace its boundary with a pencil.
• Count complete squares, half squares, and more than half squares within the boundary.
• Ignore squares less than half filled.
• The sum of the areas of complete and incomplete squares gives the approximate area of the irregular object.

Volume

• Space occupied by an object.
• Cubic metre (m³) is the SI unit.
• One cubic metre is the volume of a cube with 1-metre sides.

Density

• Mass per unit volume of a substance.
• Measured in g/cm³ or kg/m³.
• Relative density is the ratio of substance density to water density.

Area

• The amount of flat surface occupied by a closed figure.
• Measured in square units (e.g. cm²).
• Formulas exist for calculating areas of regular shapes like squares, rectangles, circles, triangles, cylinders, and spheres.

Speed

• Distance traveled per unit time.
• SI unit is meter per second (m/s).
• Uniform motion has constant speed, non-uniform motion has varying speed.
• Speed is measured by a speedometer.

Measuring Volume

• Smaller units: cm³, dm³
• 1 m³ = 10⁶ cm³ = 10³ dm³
• Volume of a cuboid is length x breadth x height.
• Measuring an irregular solid's volume involves water displacement in a measuring cylinder.

Measuring Area

• Using graph paper:
  • Place the figure on the graph paper.
  • Count complete squares, half squares, and more than half squares.
  • Ignore squares less than half.
  • Sum the areas of complete and incomplete squares (counting half squares as 0.5).

Density of Water

• Density increases when water is heated from 0°C to 4°C, reaching its maximum.
• Density decreases when water is heated from 4°C to 10°C.
• Density of water at 4°C is 1 g/cm³ or 1000 kg/m³.

Volume

• The amount of space an object occupies is its volume.
• The standard unit of volume is the cubic meter (m³).
• 1 cubic meter is the volume of a cube with 1-meter sides.
• Smaller units: cubic centimeter (cm³) and cubic decimeter (dm³).
• 1 m³ = 10⁶ cm³
• 1 m³ = 10³ dm³

Density

• Density is a substance’s mass per unit volume.
• Common unit: g/cm³ or kg/m³
• Relative density: Density of the substance divided by the density of water.
• Density can change for gases and liquids depending on temperature.

Measuring Area

• Area is the amount of flat surface space a closed figure covers.
• To measure an irregular figure, you need graph paper and the following steps:
  • Place the figure on graph paper.
  • Trace its outline.
  • Count full squares, half squares, and squares more than half-full.
  • Ignore squares less than half-full.
  • Add the areas of the full and more-than-half squares to get the approximate figure's area.
• Formulas for regular shapes:
  • Square: side²
  • Rectangle: length × breadth
  • Circle: π × (radius)²
  • Cylinder: 2π × (radius) × length
  • Sphere: 4π × (radius)²
  • Triangle: 1/2 × base × height

Speed

• Speed is distance traveled divided by the time taken to cover that distance.
• Uniform motion: constant speed throughout the journey.
• Non-uniform motion: varying speed during travel.
• Speed is measured by a speedometer.
• Distance traveled is measured by an odometer.
• Speed x Time = Distance covered
• For a fixed distance, less time means higher speed.
• For a fixed time interval, greater distance means higher speed.
• The SI unit of speed is meters per second (m/s).

Measuring the Volume of Irregular Solids

• Use a measuring cylinder and the displacement method:
  • Fill the cylinder partially with water and note the initial water level (V1).
  • Submerge the irregular solid completely in the water and note the new water level (V2).
  • The volume of the solid is V2 – V1.

Density of Water

• Water's density is highest at 4°C (1 g/cm³ or 1000 kg/m³).
• Heating water from 0°C to 4°C causes it to contract, increasing density.
• Heating water from 4°C to 10°C causes it to expand, decreasing density.

Test your understanding of key concepts related to volume, density, area, and speed. This quiz covers definitions, units, and formulas essential for mastering these fundamental physics topics. Prepare to apply your knowledge and calculations skills effectively!