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- https://math.libretexts.org/Courses/Las_Positas_College/Math_for_Liberal_Arts/09%3A_Geometry/9.02%3A_PolygonsThe sum of the three angles of a triangle is 180°. One of the angles has a measure of 90° as it is a right triangle. Since the sum of the interior angles of any triangle is 180° and there are two tria...The sum of the three angles of a triangle is 180°. One of the angles has a measure of 90° as it is a right triangle. Since the sum of the interior angles of any triangle is 180° and there are two triangles in a quadrilateral, the sum of the angles for each quadrilateral is 360°.
- https://math.libretexts.org/Courses/Santiago_Canyon_College/HiSet_Mathematica_(Lopez)/12%3A_Geometria/12.03%3A_Volumen_de_Solidos_GeometricosVivir en un mundo bidimensional sería bastante aburrido. Agradecidamente, todos los objetos físicos que ves y usas todos los días —computadoras, teléfonos, autos, zapatos— existen en tres dimensiones....Vivir en un mundo bidimensional sería bastante aburrido. Agradecidamente, todos los objetos físicos que ves y usas todos los días —computadoras, teléfonos, autos, zapatos— existen en tres dimensiones. En el mundo de la geometría, es común ver figuras tridimensionales. Los poliedros son formas que tienen cuatro o más caras, siendo cada una un polígono. Estos incluyen cubos, prismas y pirámides. A veces incluso se pueden ver figuras individuales que son compuestos de dos de estas figuras.
- https://math.libretexts.org/Bookshelves/Applied_Mathematics/Math_For_Liberal_Art_Students_2e_(Diaz)/06%3A_Geometry/6.03%3A_Volume_of_Geometric_SolidsLiving in a two-dimensional world would be pretty boring. Thankfully, all of the physical objects that you see and use every day—computers, phones, cars, shoes—exist in three dimensions. In the world ...Living in a two-dimensional world would be pretty boring. Thankfully, all of the physical objects that you see and use every day—computers, phones, cars, shoes—exist in three dimensions. In the world of geometry, it is common to see three-dimensional figures. Polyhedrons are shapes that have four or more faces, each one being a polygon. These include cubes, prisms, and pyramids. Sometimes you may even see single figures that are composites of two of these figures.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_II%3A_Integral_Calculus/02%3A_Applications_of_Integration/2.02%3A_Determining_Volumes_by_Slicing/2.2E%3A_Exercises_for_Section_2.2This page covers volume calculation techniques for 3D shapes using slicing and disk methods, including integration methods for spheres, cones, and more. It contrasts disk and washer methods for volume...This page covers volume calculation techniques for 3D shapes using slicing and disk methods, including integration methods for spheres, cones, and more. It contrasts disk and washer methods for volume determination and includes examples of pyramids and frustums. Additionally, it explores volume calculations for regions bounded by curves rotated around axes, utilizing integration and providing formulas in cubic units.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_II%3A_Integral_Calculus/02%3A_Applications_of_Integration/2.03%3A_Volumes_of_Revolution_-_Cylindrical_Shells/2.3E%3A_Exercises_for_Section_2.3This page discusses exercises on calculating volumes generated by rotating areas between curves using shell and washer methods, including examples like y=3x and y=2x3. It covers various mathe...This page discusses exercises on calculating volumes generated by rotating areas between curves using shell and washer methods, including examples like y=3x and y=2x3. It covers various mathematical graphs and shapes like spheres, cones, and ellipses, providing specific volume calculations and encouraging the use of technology for graphing.
- https://math.libretexts.org/Courses/Chabot_College/Math_in_Society_(Zhang)/02%3A_Geometry/2.03%3A_Volume_of_Geometric_SolidsLiving in a two-dimensional world would be pretty boring. Thankfully, all of the physical objects that you see and use every day—computers, phones, cars, shoes—exist in three dimensions. In the world ...Living in a two-dimensional world would be pretty boring. Thankfully, all of the physical objects that you see and use every day—computers, phones, cars, shoes—exist in three dimensions. In the world of geometry, it is common to see three-dimensional figures. Polyhedrons are shapes that have four or more faces, each one being a polygon. These include cubes, prisms, and pyramids. Sometimes you may even see single figures that are composites of two of these figures.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_I%3A_Differential_Calculus/04%3A_Applications_of_Derivatives/4.08%3A_Applied_Optimization_Problems/4.8E%3A_Exercises_for_Section_4.8This page presents a series of optimization exercises in calculus focused on identifying maximum and minimum values of functions through derivatives, endpoints, and critical points. It includes geomet...This page presents a series of optimization exercises in calculus focused on identifying maximum and minimum values of functions through derivatives, endpoints, and critical points. It includes geometric problems related to maximizing volume, minimizing areas, and optimizing dimensions, alongside practical applications in economics such as maximizing agricultural yield and profits in real estate.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_IV%3A_Multivariable_Calculus/03%3A_Vector_Calculus/3.07%3A_Surface_Integral/3.7E%3A_ExercisesThis page covers exercises in surface integrals, including calculations over specific surfaces (hemispheres, squares, triangles, spheres, and planes), with key results on mass and integrals like \(\ii...This page covers exercises in surface integrals, including calculations over specific surfaces (hemispheres, squares, triangles, spheres, and planes), with key results on mass and integrals like ∬. It also explores geometric applications in physics, such as lamina masses, forces in fluids, and heat flow, along with methods for computing total outward flux across surfaces.
