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Volume of objects with known cross sections AP Calculus Name: Area formulas you need to know: 1 1) semi-circle = (radius ) 2 2 2) rectangle of height H = (base)(height) 3) square = (base)2 4) right isosceles triangle h2 if the hypotenuse (h) is the distance between the curves the area of the triangle = 4 L2 if one of the legs (L) is the distance between the curves, the area of the triangle = 2 1) Suppose the space defined by the intersection between the functions f(x) = x2 – 1 and g(x) = x + 1 is the base of a solid that is formed by building up with the following shapes perpendicular to the x-axis. Set up the integral expression that would determine that shape’s volume: a) squares b) rectangles of height 10 c) semi-circles 1) continued: d) right isosceles triangles, with a leg on the base e) right isosceles triangles, with a hypotenuse on the base 2) Suppose the space defined by the intersection between the equations y = x, y = 6 x , and y = 0 is the bottom of a solid that is formed by building up with cross sections that are perpendicular to the y-axis with the following shapes. Set up the integral expression that would find its volume a) semi-circles: b) rectangles that are twice as tall as they are wide http://mathdemos.org/mathdemos/sectionmethod/sqrcross75slab.gif