Overview
Most area and volume questions are formula-based. Master the formulas and you’ll solve nearly all easy and medium problems. Harder problems add layers of setup but still rely on the same core formulas.
Advanced Problem Types
- Scaling: Understand how dimension changes affect area (squared) and volume (cubed).
- Backsolving: Find missing dimensions when area or volume is given.
- Coordinates: Use distance formula and base-height triangles to calculate area.
- Shape in a Shape: Handle composite or inscribed figures, subtract overlapping volumes.
- Shared Shape Faces: Combine figures while adjusting for overlapping surface area.
1. Area of 2D Shapes
- Rectangles & Squares: A = l × w
- Triangles: A = ½ × b × h
- Circles: A = π × r²
- Composite Figures: Break into known shapes or subtract areas
2. Surface Area of 3D Shapes
- Cubes & Prisms: Add up all face areas
- Cylinders, Cones, Spheres: Apply lateral/total surface area formulas
- Real-World Applications: Packaging, coverings, and dimensions
3. Volume of 3D Shapes
- Prisms & Cylinders: V = Bh or V = πr²h
- Pyramids & Cones: V = ⅓Bh
- Spheres: V = ⁴⁄₃πr³
- Composite Solids: Combine or subtract volumes
4. Applications & Transformations
- Scaling Shapes: Apply coefficients to formulas; area grows with square, volume with cube
- Relative Dimensions: Use algebra to work with variables like "height is 4 more than radius"
- Similarity: All linear dimensions scale equally to preserve shape
- Shared Faces: Subtract or add shared surface area or volume accordingly