1/14/20131Math 104 – Rimmer6.1 Volumes by SlicingGoal: To find the volume of a solid using second semester calculus • Volume by Cross-Sections• Volume by Disk• Volume by Washer• Volume by ShellsVolume by SlicingMath 104 – Rimmer6.1 Volumes by Slicing6.1 Volumes by SlicingGoal: To find the volume of a solid Method: “Cutting”the solid into many “pieces”, find the volume of the pieces and add to find the total volume. • The “pieces”are treated are cylinders. • The base of each cylinder is called a cross-section.
1/14/2013Math 104 – Rimmer6.1 Volumes by Slicing6.1 Volumes• The volume of each cylinder is found by taking the area of the cross-section, A(xi*), and multiplying by the height, Δx. • Taking the limit as the number of cylinders goes to infinity gives the exact volume of the solid. • The volume of the solid can be approximated by the sum of all cylinders.()*1niiVA xx=≈Δ∑()*1limniniVA xx→∞==Δ∑()baVA x dx⇒=∫Math 104 – Rimmer6.1 Volumes by SlicingA solid has a circular base of radius 4. If every plane cross section perpendicular to the x-axis is a square, then find the volume of the solid.22=