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Showing posts from October, 2023

stereometry - based on stereometry chapter of handbook for BSATU abiturient (Математика абитуриенту: справочное пособие Минск : БГАТУ, 2008 сост Морозова)

crossection  2D plane(shape) with intersection of 3D shape(figure) - crosssection of solid Horizontal crossection Vertical crossection *of sphere **also exist different/other types of crossections(with random angles, complex planes) polyhedrons polygon - shape built by line segments Prism Based on an n-angle polygon, with two connected parallel bases *lines of connection are shaping parallelograms Formulas S(all) = 2*S(base)+ S(side) S(side) - n*shape V = S(of the base or horizontal crossection)*l *l - side edge *S - surface area *V - volume  Straight & regular prism Diagonal in straight: d = a^2*b^2*l^2, l = h *straigh with straigh angles to base Cube *all edges are equal Pyramid Straight and regular pyramid *in straight - top vertex above the centroid of the base Formulas S(all) = S(sides)+S(base) S(side) - S of triangle V = ⅓*S(base)*h *h - height **for proof V: Build cube with diagonals - will see 6 equal pyramids Volume of cube = a*b*c; S(base) = a*b; c = H In one pyr...