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Volume, area and converting units

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Apuntes de la lección

What is Volume?

  • Volume is the amount of space a 3D shape takes up.
  • Think of a box: volume tells you how much it can hold.
  • We measure volume in cubic units, like cubic centimetres (cm3).
  • A unit cube is a cube with sides of 1 unit, like 1 cm. Its volume is 1 cm3.
  • To find volume, we count how many unit cubes fit inside the shape.

Units of Length, Area, and Volume

  • Length is measured in units like centimetres (cm) or metres (m).
  • Area is measured in square units, like square centimetres (cm2).
  • Volume is measured in cubic units, like cubic centimetres (cm3).
  • Remember: cm for length, cm2 for area, cm3 for volume.
  • A square with side 1 cm has area 1 cm2. A cube with side 1 cm has volume 1 cm3.

Converting Units of Length

  • To convert between units, use conversion factors.
  • For length: 1 m = 100 cm, 1 km = 1000 m.
  • To go from a larger unit to a smaller one, multiply.
  • Example: 3 m = 3 × 100 = 300 cm.
  • To go from a smaller unit to a larger one, divide.
  • Example: 500 cm = 500 ÷ 100 = 5 m.

Converting Units of Area

  • Area units convert by squaring the length conversion factor.
  • Since 1 m = 100 cm, then 1 m2 = 100 × 100 = 10,000 cm2.
  • To convert from m2 to cm2, multiply by 10,000.
  • Example: 2 m2 = 2 × 10,000 = 20,000 cm2.
  • To convert from cm2 to m2, divide by 10,000.
  • Example: 50,000 cm2 = 50,000 ÷ 10,000 = 5 m2.

Converting Units of Volume

  • Volume units convert by cubing the length conversion factor.
  • Since 1 m = 100 cm, then 1 m3 = 100 × 100 × 100 = 1,000,000 cm3.
  • To convert from m3 to cm3, multiply by 1,000,000.
  • Example: 2 m3 = 2 × 1,000,000 = 2,000,000 cm3.
  • To convert from cm3 to m3, divide by 1,000,000.
  • Example: 3,000,000 cm3 = 3,000,000 ÷ 1,000,000 = 3 m3.

Finding Volume of a Cuboid

  • A cuboid is a box shape with 6 rectangular faces.
  • To find its volume, use the formula: V = l × w × h.
  • Here, V = volume, l = length, w = width, h = height.
  • Measure all sides in the same unit, then multiply.
  • Example: A box with l = 5 cm, w = 3 cm, h = 2 cm has V = 5 × 3 × 2 = 30 cm3.
  • You can also find volume by multiplying the area of the base by the height.

Volume by Base Area

  • The base is the bottom face of a cuboid.
  • The area of the base is length × width.
  • Then multiply by the height: V = base area × h.
  • This works because stacking base layers fills the height.
  • Example: If base area = 12 cm2 and h = 4 cm, then V = 12 × 4 = 48 cm3.

Adding Volumes of Combined Shapes

  • Sometimes a solid is made of two cuboids stuck together.
  • Find the volume of each cuboid separately.
  • Then add the volumes to get the total volume.
  • Example: Cuboid A has volume 20 cm3, cuboid B has volume 15 cm3, total = 35 cm3.
  • Make sure to use the same unit for both volumes.

Area vs Perimeter vs Volume

  • Perimeter is the distance around a 2D shape. Measured in units like cm.
  • Area is the space inside a 2D shape. Measured in square units like cm2.
  • Volume is the space inside a 3D shape. Measured in cubic units like cm3.
  • Perimeter is for 2D shapes only; area is for 2D shapes; volume is for 3D shapes.
  • Example: A rectangle has perimeter = 2 × (length + width), area = length × width. A box has volume = length × width × height.

Diapositivas

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Preguntas de práctica

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  1. 1.What is volume?

    Easy
    • AThe amount of space a 3D shape takes up
    • BThe distance around a shape
    • CThe amount of surface a shape covers
    • DThe weight of an object

  2. 2.Which unit is used for volume?

    Easy
    • Acm
    • Bcm2
    • Ccm3
    • Dg

  3. 3.Area is measured in square units, like cm2.

    Easy

    True or false?

  4. 4.A cuboid has length 5 cm, width 3 cm, and height 2 cm. What is its volume?

    Easy
    • A10 cm3
    • B15 cm3
    • C30 cm3
    • D60 cm3

  5. 5.Which of the following are correct statements about units? (select all that apply)

    Medium
    • A1 m = 100 cm
    • B1 m2 = 100 cm2
    • C1 m3 = 1000 cm3
    • D1 L = 1000 mL
    • E1 cm3 = 1 mL

  6. 6.Put these units in order from smallest to largest volume.

    Medium
    • 1 cm3
    • 1 mL
    • 1 L
    • 1 m3

  7. 7.Match each measurement to the correct unit.

    Medium
    • Length
    • Area
    • Volume
    • cm
    • cm2
    • cm3

  8. 8.Which of these are correct conversions? (select all that apply)

    Medium
    • A1 L = 1000 mL
    • B1 m = 100 cm
    • C1 cm³ = 1 mL
    • D1 m³ = 1000 cm³

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