Geometry formula sheet with quick checks
A compact map of the area and volume formulas you actually use in secondary geometry.
Key formulas
Plane formulas
Triangle area = (1/2) × base × corresponding height. Circle circumference = 2πr and area = πr². Trapezium area = (1/2)(a + b)h, where a and b are the parallel sides.
Solid formulas
Prism volume = cross-sectional area × length. Pyramid volume = (1/3) of the related prism. Cylinder: πr²h. Cone: (1/3)πr²h. Sphere: (4/3)πr³.
Numerical check
A cylinder with r = 3 cm and h = 8 cm has volume π × 9 × 8 = 72π cm³. A sphere with r = 3 cm has volume (4/3)π × 27 = 36π cm³. Compare units: area is square, volume is cubic.
Worked example
Worked example
Problem. A circle has radius 7 cm. Find its area and the volume of a cylinder with the same radius and height 10 cm. Leave answers in terms of π.
Solution. Circle area = πr² = 49π cm². Cylinder volume = πr²h = 49π × 10 = 490π cm³.
Unit conversion
1000 cm³ = 1 litre. So a 250 cm³ answer is 0.25 litres.
Review quiz
Which formula gives sphere volume?
Practice questions
- Find the area of a triangle with base 14 cm and height 9 cm.
- Find the volume of a cone with radius 4 cm and height 9 cm in terms of π.
Study notes
Should I memorise every formula at once?
Memorise the ones tied to your current topic, and keep a one-page map for the rest.
Why keep π unevaluated?
Exact answers in terms of π avoid early rounding errors.