The base of a three-dimensional figure is bound by the line y = -x + 3 on the interval [-1, 1]. Vertical cross sections that are perpendicular to the x-axis are right triangles with a height equal to 6. Algebraically, find the area of each triangle. X -3-2 -14 19 1 2 3 4 5 6 7 -2- O A(x) = 2(-X + 3)(6) O A(X) = (-X + 3)(6) O A(X) = = (-X + 3)(6) O A(y) = ; (-y + 3)(6)The base of a three-dimensional figure is bound by the circle x2 + y2 = 4. Vertical cross sections that are perpendicular to the x-axis are squares. Algebraically, find the area of each square. X 5432 2345 In to do is O A(X) = 4+ 2x2 O A(x) = 4 - 2x2 O A(x) = 16 - 4x2 O A(x) = 16 + 4x2The base of a three-dimensional figure is bound by the semi-circle y = 19 - a2 . Vertical cross sections that are perpendicular to the x-axis are squares. Algebraically, find the area of each square. Y X 5432-1 1 2345 -+ O A(x) = 2(9 - x2) O A(x) = 4(9 - x2) O A(X) = = (9-x2) O A(X) = (9-x2)The base of a three-dimensional figure is bound by the graph x = cos(y) + 1 on the interval [-TI, T]. Vertical cross sections that are perpendicular to the y-axis are squares. Algebraically, find the area of each square. Y -NWA UI X 5432-141 2345 Int dok O A(y) = (cos(y) + 1) O A(y) = 1 (cos(y) + 1)2 O A(y) = (sin(y) + 1)2 O A(y) = (cos(y) + 1)2The base of a three-dimensional gure is bound by the graph x = W on the interval ['1, 4]. Vertical cross sections that are perpendicular to the xaxis are rectangles with the height equal to one-half the width. Algebraically, nd the area of each rectangle. O A(y)=%y O A(y)=y2 O Am=y2 The base of a three-dimensional figure is bound by the line y = 2x + 1 on the interval [1, 3]. Vertical cross sections that are perpendicular to the base are right triangles with a height equal to 4. Find the volume of the figure using i = five slices. AY -NWAUIDO X -10 1 234 56 7 8 5 O V= E A (c ) . Ax i=1 5 O V= E A (G ) O V= LY 21 1 EA(G) . Ax O V = E A (G) . AxThe base of a three-dimensional gure is bound by the line y = a: l 2 on the interval [-1, 1]. Vertical cross sections that are perpendicular to the xaxis are rectangles with a height equal to one-half the width. Find the volume of the gure. O V=4.'131 O V=2.797 _ 5 O V'E The base of a three-dimensional figure has a base bound by the y-axis and the line x = y + 4 on the interval [-2, 1]. Vertical cross sections that are perpendicular to the y-axis are squares. Find the numerical volume of the figure. W X 4567 O V= 31 2 O V = 39 O V= 31 3 O V 31The base of a three-dimensional gure is bound by the x-axis and the curve y = e\" on the interval [-1, 1]. Vertical cross sections that are perpendicular to the xaxis are right triangles with a height equal to 4. Find the numerical volume of the gure. 543421." 123 45 O V = 5.436 O V = 4.701 O V = 4.500 O V = 2.900 The base of a three-dimensional figure is bound by the y-axis and the curve x = -3y2 + 6 on the interval [-1, 1]. Vertical cross sections that are perpendicular to the y-axis are right triangles with a height equal to 6. Find the numerical volume of the figure. X 6 7 O V = 48 O V = 30 O V = 45 3 O V= 64