Math 104 6.1 Notes - Math 104 Rimmer 6.1 Volumes by Slicing Goal To find the volume of a solid using second semester calculus Volume by Cross-Sections

Math 104 6.1 Notes - Math 104 Rimmer 6.1 Volumes by Slicing...

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1/14/2013 1 Math 104 – Rimmer 6.1 Volumes by Slicing Goal : To find the volume of a solid using second semester calculus • Volume by Cross-Sections • Volume by Disk • Volume by Washer • Volume by Shells Volume by Slicing Math 104 – Rimmer 6.1 Volumes by Slicing 6.1 Volumes by Slicing Goal : 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 .
1/14/2013 Math 104 – Rimmer 6.1 Volumes by Slicing 6.1 Volumes • The volume of each cylinder is found by taking the area of the cross-section, A ( x i * ) , and multiplying by the height, Δ x . • 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. ( ) * 1 n i i V A x x = Δ ( ) * 1 lim n i n i V A x x →∞ = = Δ ( ) b a V A x dx = Math 104 – Rimmer 6.1 Volumes by Slicing A 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. 2 2 =

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