Answer with graph A solid has a base in the form of an ellipse with major axis 10 and minor axis 8. Find its volume if everysection perpendicular to the major axis is an isosceles right triangle with one leg in the plane of thebase.Ans. 640/3 cubic unitsThe base of a solid is the segment of the parabola y 12x cut off by the latus rectum. A section of thesolid perpendicular to the axis of the parabola is a square. Find its volume.%3DAns. 216 cubic unitsThe base of a solid is the first-quadrant area bounded by the line 4x + 5y = 20 and the coordinate axes.Find its volume if every plane section perpendicular to the x axis is a semicircle.Ans.107/3 cubic unitsThe base of a solid is the circle x+ y = 16x, and every plane section perpendicular to the x axis is arectangle whose height is twice the distance of the plane of the section from the origin. Find itsvolume.%3DAns. 1024 T cubic unitsA horm-shaped solid is generated by moving a circle, having the ends of a diameter on the first-quadrantarcs of the parabolas y+ 8x = 64 and y+ 16x = 64, parallel to the xz plane. Find the volumegenerated.Ans. 2567/15 cubic unitsThe vertex of a cone is at (a, 0, 0), and its base is the circle y +z - 2by 0, x = 0. Find itsvolume.Ans. rab? cubic unitsFind the volume of the solid bounded by the paraboloid y + 4z = x and the plane x = 4.Ans.47 cubic unitsA barrel has the shape of an ellipsoid of revolution with equal pieces cut from the ends. Find its volumeif its height is 6 ft, its midsection has radius 3 ft, and its ends have radius 2 ft.Ans. 447 ftThe section of a certain solid cut by any plane perpendicular to the x axis is a circle with the ends of a= 9x and x' = 9y. Find its volume.diameter lying on the parabolas yAns. 6561 7/280 cubic unitsThe section of a certain solid cut by any plane perpendicular to the x axis is a square with the ends of adiagonal lying on the parabolas y = 4x and x = 4y. Find its volume.Ans.144/35 cubic unitsA hole of radius 1 inch is bored through a sphere of radius 3 inches, the axis of the hole being a diameterof the sphere. Find the volume of the sphere which remains.Ans. 64 V2/3 in'

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A solid has a base in the form of an ellipse with major axis 10 and minor axis 8. Find its volume if every section perpendicular to the major axis is an isosceles right triangle with one leg in the plane of the base. Ans. 640/3 cubic units The base of a solid is the segment of the parabola y² = 12x cut off by the latus rectum. A section of the solid perpendicular to the axis of the parabola is a square. Find its volume. Ans. 216 cubic units The base of a solid is the first-quadrant area bounded by the line 4x + 5y = 20 and the coordinate axes. Find its volume if every plane section perpendicular to the x axis is a semicircle. Ans. 1077/3 cubic units The base of a solid is the circle x² + y² = 16x, and every plane section perpendicular to the x axis is a rectangle whose height is twice the distance of the plane of the section from the origin. Find its volume. Ans. 1024 π cubic units A horn-shaped solid is generated by moving a circle, having the ends of a diameter on the first-quadrant the parabolas y² + 8x = 64 and y² + 16x = 64, parallel to the xz plane. Find the volume generated. arcs Ans. 256/15 cubic units The vertex of a cone is at (a,0,0), and its base is the circle y² + 2² - 2by=0, x=0. Find its volume. Ans.mab² cubic units Find the volume of the solid bounded by the paraboloid y² + 4z² = x and the plane x = 4. Ans. 477 cubic units A barrel has the shape of an ellipsoid of revolution with equal pieces cut from the ends. Find its volume if its height is 6 ft, its midsection has radius 3 ft, and its ends have radius 2 ft. Ans. 447 ft³ The section of a certain solid cut by any plane perpendicular to the x axis is a circle with the ends of a diameter lying on the parabolas y² = 9x and x² =9y. Find its volume. Ans. 6561 T/280 cubic units The section of a certain solid cut by any plane perpendicular to the x axis is a square with the ends of a diagonal lying on the parabolas y2 = 4x and x² = 4y. Find its volume. Ans. 144/35 cubic units A hole of radius 1 inch is bored through a sphere of radius 3 inches, the axis of the hole being a diameter of the sphere. Find the volume of the sphere which remains. Ans. 64√2/3 in³