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 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.

800
1200
1600
2000
2400
2800
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

More geometry concepts

3D geometryaltitudeangle bisectorangle bisector theoremangle chasingangle sumannulusarcareaarea decompositionarea ratioBrahmagupta’s FormulaBritish Flag TheoremcentroidCeva’s Theoremchordcirclecircle 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