Power scaling of length, area, and volume — AMC & AIME Problems
Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses power scaling of length, area, and volume — 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.
All of these problems are used with official legal permission of the Mathematical Association of America (MAA).
AMC 8
1997 AMC 8 Problem 22 · 2001 AMC 8 Problem 8 · 2001 AMC 8 Problem 9 · 2002 AMC 8 Problem 13 · 2010 AMC 8 Problem 10 · 2018 AMC 8 Problem 15 · 2025 AMC 8 Problem 18
AMC 10
2007 AMC 10B Problem 23 · 2008 AMC 10B Problem 7 · 2010 AMC 10A Problem 12 · 2013 AMC 10B Problem 15 · 2016 AMC 10B Problem 10 · 2025 AMC 10B Problem 19
More geometry concepts
3D geometryaltitudeangle bisectorangle bisector theoremangle chasingangle sumannulusarcareaarea decompositionarea ratioBrahmagupta’s Formulacentroidchordcirclecircle areacircumcircle, circumcenter, and circumradiuscircumferenceconecongruence (geometry)coordinate geometrycube geometrycyclic quadrilateralcylinderdiagonaldistance formulaellipseequiangular polygonequilateral triangleEuler’s Polyhedron FormulaHeron’s Formulahomothetyhyperbolaincircle, incenter, and inradiusinscribed angleisosceles trianglekitelattice pointlaw of cosineslaw of sinesmass pointsmedian (geometry)midpointnet (3D geometry)paper foldingparabolaparallel linesparallelogramperimeterperpendicular bisectorPick’s Theorempolyhedronpower of a pointPtolemy’s TheorempyramidPythagorean TheoremPythagorean Tripleradical axisrectanglerectangular prismreflection (geometry)regular polygonrhombusright trianglesectorshoelace formulasimilarityspecial right trianglespheresquare (geometry)Stewart’s Theoremsurface areatangent circlestangent linetransformationtrapezoidtriangle areatriangle inequalitytrigonometric identitytrigonometryvectorViviani’s Theoremvolume