3D shapes, volume and surface area

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교육자를 위해: 3D shapes, volume and surface area(KS3 Maths, Geometry & Measures)을(를) 위한 바로 쓸 수 있는 수업 슬라이드, 복습 노트 — 수업에 사용하거나, 학습자들이 실시간 게임으로 즐기는 인터랙티브 클래스 활동으로 진행하세요.

수업 노트

Faces, Edges and Vertices

  • A face is a flat surface of a 3D shape.
  • An edge is a line where two faces meet.
  • A vertex (plural: vertices) is a point where edges meet.
  • For a cuboid: 6 faces, 12 edges, 8 vertices.
  • For a cube: 6 faces, 12 edges, 8 vertices.
  • For a cylinder: 3 faces (2 circular, 1 curved), 2 edges, 0 vertices.
  • For a sphere: 1 curved face, 0 edges, 0 vertices.
  • For a square-based pyramid: 5 faces, 8 edges, 5 vertices.

Nets of 3D Shapes

  • A net is a 2D shape that folds up to make a 3D shape.
  • A cube net is made of 6 squares.
  • A cuboid net is made of 6 rectangles (3 pairs of identical rectangles).
  • A cylinder net is made of 2 circles and 1 rectangle.
  • A square-based pyramid net is made of 1 square and 4 triangles.
  • A triangular prism net is made of 2 triangles and 3 rectangles.

Plans and Elevations

  • A plan is the view from above (bird's-eye view).
  • A front elevation is the view from the front.
  • A side elevation is the view from the side.
  • Plans and elevations are 2D drawings that show the shape of a 3D object from different directions.
  • They are used in design and architecture to describe 3D objects accurately.

Volume of Cubes and Cuboids

  • Volume is the amount of space inside a 3D shape.
  • Volume is measured in cubic units, e.g. cm3, m3.
  • Volume of a cube: V = s3, where s = side length.
  • Volume of a cuboid: V = l × w × h, where l = length, w = width, h = height.
  • Example: a cuboid with l = 5 cm, w = 3 cm, h = 2 cm has V = 5 × 3 × 2 = 30 cm3.

Volume of Prisms

  • A prism is a 3D shape with the same cross-section all along its length.
  • Volume of a prism: V = A × l, where A = area of cross-section, l = length.
  • The cross-section is the shape you see when you slice the prism parallel to its base.
  • Example: a triangular prism with cross-section area 12 cm2 and length 10 cm has V = 12 × 10 = 120 cm3.
  • Cubes and cuboids are special types of prism.

Volume of Cylinders

  • A cylinder is a prism with a circular cross-section.
  • Volume of a cylinder: V = π r2 h, where r = radius, h = height.
  • Example: a cylinder with r = 3 cm and h = 10 cm has V = π × 32 × 10 = 90π cm3 ≈ 282.7 cm3.
  • Use π ≈ 3.14 or the π button on your calculator.

Surface Area of Cuboids

  • Surface area is the total area of all the faces of a 3D shape.
  • Surface area is measured in square units, e.g. cm2, m2.
  • A cuboid has 6 rectangular faces; opposite faces are identical.
  • Surface area of a cuboid: SA = 2(lw + lh + wh), where l = length, w = width, h = height.
  • Example: a cuboid with l = 5 cm, w = 3 cm, h = 2 cm has SA = 2(5×3 + 5×2 + 3×2) = 2(15 + 10 + 6) = 62 cm2.

Surface Area of Prisms

  • To find the surface area of a prism, add the areas of all its faces.
  • For a prism, the two end faces are identical (the cross-section).
  • The other faces are rectangles; their total area is perimeter of cross-section × length.
  • Surface area of a prism: SA = 2A + P × l, where A = area of cross-section, P = perimeter of cross-section, l = length.
  • Example: a triangular prism with cross-section area 12 cm2, perimeter 16 cm, length 10 cm has SA = 2×12 + 16×10 = 24 + 160 = 184 cm2.

Surface Area of Cylinders

  • A cylinder has 2 circular faces and 1 curved surface.
  • The curved surface unfolds into a rectangle with width = circumference of the circle (2πr) and height = h.
  • Surface area of a cylinder: SA = 2πr2 + 2πrh, where r = radius, h = height.
  • Example: a cylinder with r = 3 cm and h = 10 cm has SA = 2π×32 + 2π×3×10 = 18π + 60π = 78π cm2 ≈ 245.0 cm2.

Capacity and Litres

  • Capacity is the amount a container can hold.
  • Capacity is often measured in litres (L) or millilitres (mL).
  • 1 litre = 1000 millilitres.
  • 1 litre = 1000 cm3.
  • 1 millilitre = 1 cm3.
  • 1 m3 = 1000 litres.
  • To convert from cm3 to litres, divide by 1000.
  • To convert from litres to cm3, multiply by 1000.

슬라이드

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연습 문제

무료 미리 보기 — 65개 중 8개 문제. 가입하면 전부 볼 수 있어요.

  1. 1.Which of these is an SI derived unit of volume?

    Easy
    • Acubic metre
    • Bkilogram
    • Cnewton
    • Dmetre

  2. 2.The volume of a container is generally understood to be its capacity. Which statement describes capacity?

    Easy
    • AThe amount of fluid the container could hold
    • BThe amount of space the container itself displaces
    • CThe total length of all its edges
    • DThe total area of all its faces

  3. 3.A cube has edge length 1 dm. What is its volume in litres?

    Easy
    • A1 litre
    • B10 litres
    • C0.1 litres
    • D1000 litres

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

    Medium
    • A60 cm3
    • B12 cm3
    • C47 cm3
    • D94 cm3

  5. 5.A prism has a cross-sectional area of 12 cm2 and a length of 9 cm. What is its volume?

    Medium
    • A108 cm3
    • B21 cm3
    • C54 cm3
    • D216 cm3

  6. 6.A cylinder has radius 3 cm and height 10 cm. Using π = 3.14, what is its volume to 1 decimal place?

    Medium
    • A282.6 cm3
    • B94.2 cm3
    • C188.4 cm3
    • D565.2 cm3

  7. 7.A cuboid has length 8 cm, width 5 cm and height 2 cm. What is its total surface area?

    Medium
    • A132 cm2
    • B80 cm2
    • C66 cm2
    • D264 cm2

  8. 8.A cylinder has radius 4 cm and height 7 cm. Using π = 3.14, what is its total surface area to 1 decimal place?

    Hard
    • A276.3 cm2
    • B175.8 cm2
    • C351.7 cm2
    • D100.5 cm2

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