Year 7 Exam > Year 7 Notes > Year 7 Mathematics (Cambridge) > Shapes, Area and Volume
Shapes, Area and Volume | Year 7 Mathematics (Cambridge) PDF Download
Understanding Different Shapes
Shapes can be classified into two-dimensional (2D) and three-dimensional (3D).
- Two-Dimensional Shapes:
- Examples include squares, rectangles, triangles, circles, and polygons.
- Each shape has specific properties like sides, angles, and symmetry.
- Understanding properties helps in calculating their area.
- Three-Dimensional Shapes:
- Examples include cubes, prisms, pyramids, cylinders, and spheres.
- These shapes have volume, surface area, and various faces, edges, and vertices.
- Volume and surface area calculations involve understanding dimensions and formulas.
Calculating Area
Area of Two-Dimensional Shapes:
- Rectangle: Area = length × width
- Example: A rectangle with length 5 cm and width 3 cm has an area of 15 square centimeters.
- Triangle: Area = ½ × base × height
- Example: A triangle with base 4 cm and height 6 cm has an area of 12 square centimeters.
- Circle: Area = π × radius²
- Example: A circle with radius 2 cm has an area of approximately 12.57 square centimeters (π ≈ 3.14).
Question for Shapes, Area and VolumeTry yourself: What is the formula to calculate the area of a triangle?View Solution
Calculating Volume
Volume of Three-Dimensional Shapes:
- Cube: Volume = side length3
- Example: A cube with side length 3 cm has a volume of 27 cubic centimeters.
- Cylinder: Volume = π × radius2 × height
- Example: A cylinder with radius 2 cm and height 5 cm has a volume of approximately 62.83 cubic centimeters (π ≈ 3.14).
- Sphere: Volume = ⁴⁄₃ × π × radius3
- Example: A sphere with radius 3 cm has a volume of approximately 113.1 cubic centimeters (π ≈ 3.14).
Examples and Applications
Real-Life Applications:
- Calculating floor space using area measurements.
- Determining container volumes for liquids or solids.
- Understanding shape properties in architecture and design.
Summary
Understanding shapes, area, and volume involves recognizing their properties and applying specific formulas for calculations. These concepts are fundamental in various real-life scenarios, from construction to everyday measurements.
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