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Volume, area and converting units

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先生の方へ： Volume, area and converting units（Primary Maths、Grade 5）向けのすぐ使えるレッスンスライド, 復習ノート — レッスンで使うか、生徒がライブゲームとして遊ぶインタラクティブなクラス活動としてトピックを実施できます。

レッスンノート

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.

スライド

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練習問題

無料プレビュー — 64問中8問。すべて見るには登録を。

  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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