geometry
Cube geometry — AMC & AIME Problems
75 problems
Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses Cube geometry — a geometry concept — each with a professionally curated solution, many with a video solution too, from LIVE by Po-Shen Loh. Browse all concepts or the full past-contest archive.
LIVE focuses on challenge. As a social enterprise, we also explain standard school concepts one at a time, for free, on our sister site Expii. For this idea: Length of Space Diagonal, Volume of a Box, Surface Area of a Prism.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
Filter by difficulty
These problems’ difficulty ratings come from real solve attempts on our platform. Tap a band or a contest to filter the list below, and tap a selected band again to include all difficulties. See the full difficulty guide.
AMC 8
- 1985 AMC 8 Problem 11
- 1987 AMC 8 Problem 7
- 1989 AMC 8 Problem 23
- 1990 AMC 8 Problem 11
- 1991 AMC 8 Problem 24
- 1992 AMC 8 Problem 20
- 1997 AMC 8 Problem 17
- 1997 AMC 8 Problem 21
- 1999 AMC 8 Problem 8
- 2003 AMC 8 Problem 1
- 2006 AMC 8 Problem 18
- 2008 AMC 8 Problem 16
- 2012 AMC 8 Problem 21
- 2014 AMC 8 Problem 19
- 2015 AMC 8 Problem 12
- 2018 AMC 8 Problem 24
- 2019 AMC 8 Problem 12
- 2020 AMC 8 Problem 9
- 2024 AMC 8 Problem 20
- 2026 AMC 8 Problem 15
AMC 10
- 2002 AMC 10A Problem 18
- 2003 AMC 10A Problem 3
- 2003 AMC 10A Problem 10
- 2004 AMC 10B Problem 23
- 2005 AMC 10A Problem 11
- 2007 AMC 10A Problem 11
- 2007 AMC 10A Problem 21
- 2008 AMC 10A Problem 21
- 2009 AMC 10A Problem 24
- 2010 AMC 10A Problem 20
- 2011 AMC 10A Problem 24
- 2011 AMC 10B Problem 22
- 2012 AMC 10B Problem 23
- 2013 AMC 10A Problem 14
- 2015 AMC 10B Problem 20
- 2016 AMC 10A Problem 18
- 2016 AMC 10B Problem 17
- 2020 AMC 10A Problem 10
- 2020 AMC 10B Problem 2
- 2021 AMC 10A Fall Problem 24
- 2021 AMC 10B Fall Problem 24
- 2023 AMC 10A Problem 6
- 2024 AMC 10A Problem 24
AMC 12
- 1957 AMC 12 Problem 17
- 1972 AMC 12 Problem 12
- 1973 AMC 12 Problem 2
- 1980 AMC 12 Problem 16
- 1981 AMC 12 Problem 9
- 1982 AMC 12 Problem 16
- 1985 AMC 12 Problem 20
- 1989 AMC 12 Problem 26
- 2003 AMC 12A Problem 13
- 2004 AMC 12B Problem 20
- 2005 AMC 12A Problem 10
- 2007 AMC 12A Problem 20
- 2008 AMC 12A Problem 8
- 2008 AMC 12A Problem 11
- 2009 AMC 12B Problem 17
- 2010 AMC 12A Problem 9
- 2011 AMC 12B Problem 18
- 2012 AMC 12A Problem 22
- 2012 AMC 12B Problem 19
- 2016 AMC 12A Problem 14
- 2019 AMC 12B Problem 11
- 2021 AMC 12B Fall Problem 20
More geometry concepts
- 3D geometry
- Altitude
- Angle bisector
- Angle bisector theorem
- Angle chasing
- Angle sum
- Annulus
- Arc
- Area
- Area decomposition
- Area ratio
- Brahmagupta’s Formula
- British Flag Theorem
- Centroid
- Ceva’s Theorem
- Chord
- Circle
- Circle area
- Circumcircle, circumcenter, and circumradius
- Circumference
- Cone
- Congruence (geometry)
- Coordinate geometry
- Cyclic quadrilateral
- Cylinder
- Diagonal
- Distance formula
- Ellipse
- Equiangular polygon
- Equilateral triangle
- Euler’s Polyhedron Formula
- Heron’s Formula
- Homothety
- Hyperbola
- Incircle, incenter, and inradius
- Inscribed angle
- Isosceles triangle
- Kite
- Lattice point
- Law of cosines
- Law of sines
- Mass points
- Median (geometry)
- Midpoint
- Net (3D geometry)
- Paper folding
- Parabola
- Parallel lines
- Parallelogram
- Perimeter
- Perpendicular bisector
- Pick’s Theorem
- Polyhedron
- Power of a point
- Power scaling of length, area, and volume
- Ptolemy’s Theorem
- Pyramid
- Pythagorean Theorem
- Pythagorean Triple
- Radical axis
- Rectangle
- Rectangular prism
- Reflection (geometry)
- Regular polygon
- Rhombus
- Right triangle
- Sector
- Shoelace formula
- Similarity
- Special right triangle
- Sphere
- Square (geometry)
- Stewart’s Theorem
- Surface area
- Tangent circles
- Tangent line
- Transformation
- Trapezoid
- Triangle area
- Triangle inequality
- Trigonometric identity
- Trigonometry
- Vector
- Viviani’s Theorem
- Volume