QR: Geometry, Area & Volume

Essential Formulas

You do NOT need to memorise complex geometry formulas. The UCAT tests basic shapes:

2D Shapes

• Rectangle: Area = length × width. Perimeter = 2(length + width)
• Triangle: Area = ½ × base × height
• Circle: Area = π × r². Circumference = 2π × r (use π ≈ 3.14)
• Trapezium: Area = ½ × (a + b) × h (where a and b are parallel sides)

3D Shapes

• Cuboid: Volume = length × width × height. Surface area = 2(lw + lh + wh)
• Cylinder: Volume = π × r² × h
• Sphere: Volume = (4/3) × π × r³

Common QR Geometry Questions

• Finding the area of a composite shape (e.g., L-shape = two rectangles, or rectangle with semicircle)
• Calculating how many tiles/units fit into a space
• Finding the volume of a container and relating it to a flow rate
• Converting between units of area (1 m² = 10,000 cm²) or volume (1 m³ = 1,000,000 cm³ = 1,000 litres)
• Scaling — if dimensions double, area quadruples and volume increases by factor of 8

Unit Conversion for Area and Volume

This is a common trap:

• 1 m = 100 cm, but 1 m² = 10,000 cm² (100²), and 1 m³ = 1,000,000 cm³ (100³)
• 1 km = 1000 m, but 1 km² = 1,000,000 m²
• 1 litre = 1000 cm³ = 0.001 m³