PPT-A solid of revolution

is a solid obtained by rotating a region in the plane about an axis The right circular cone and sphere are familiar examples of such solids Each of these is swept out as a plane region revolves around an . 11 Objective: Find the volume of a solid of revolution using the Shell method. Compare to the disk method.. Miss . Battaglia. AP Calculus. Alternative to finding volume of a solid of revolution. . Called the shell method because it uses cylindrical shells.. 4-G. . Disk method. Find Volume – Disk Method. Revolve about a horizontal axis. Slice perpendicular to axis – slices vertical. Integrate in terms of x. Revolve about a vertical axis. Slice perpendicular to axis – slices horizontal. & Washer Methods. Objective: Find volume of a solid revolution using the disk method and washer method.. Miss . Battaglia. AP Calculus. Rotate around the x-axis and find the volume of y=. 1. /. 2 . Find the volume of the solid generated when the. r. egion in the first quadrant bounded by the given curve and line. i. s revolved about the . x. -axis.. (0,5). (2,25). f. (x). x. Cross-section area:. & Washer Methods. Objective: Find volume of a solid revolution using the disk method and washer method.. Miss . Battaglia. AP Calculus. Rotate around the x-axis and find the volume of y=. 1. /. 2 . 4-7 . . Comparison of Methods. Comparison of Disk and Shell Methods. The disk and shell methods can be distinguished as follows.. For the disk method, the representative rectangle is always . perpendicular . . Washers and Disks. Find Volume – Disk Method. Revolve about a horizontal axis. Slice perpendicular to axis – slices vertical. Integrate in terms of x. Revolve about a vertical axis. Slice perpendicular to axis – slices horizontal. Economic and social conditions around the world changed dramatically as result of the Industrial Revolution. Important Terms: . Do Now: . Identify two positive impacts of the Industrial Revolution. Quarterly Exam Review. And How Imitation . is . T. he . Greatest Form of Flattery. The Industrial Revolution was a significant turning point in world history. During the Industrial Revolution, machines were used to manufacture goods. Causes of the French Revolution. Abuses of the old regime. (What’s a regime?). Political (leave space to explain). Social. Economic. Political Reasons. The king was an absolute monarch. The king picked people based on favoritism. Background. Treaty of Ryswick – 1695 . Africans and . engagés. for labor. 1685 – Negro codes – punishments . High mortality / low fertility. Slave population – 500,000 – most African-born. Causes of the French Revolution What brought about the French Revolution? Enlightenment thinkers ~ many lived in France under absolute monarchy ~ spoke of change granting more rights to the people….sounded good! Page 1of 81Finding volume of a solid of revolution using a disc method2Finding volume of a solid of revolution using a washer method3Finding volume of a solid of revolution using ashell methodIf a reg