Definition of Volume of a Solid

p {margin: 0; padding: 0;} No. Date Definition of Volume of a solid" The volume of a solid with known integrable cross section area A(x) from x =a to X = 6 is integral of A from a to b, b V: A(x) dx Method of Slicing: 1) Sketch the solid and thypical cross section 2) Find a formula for V (x) (Note that V (x) is used instead of A (x)) 3) Find the limits of integration 4) Integrate V (x) to find volume This application of the method of slicing is called the method The shape of the slice is a disk, so we use the formula for the alea of a circle to find the volume of the disk. 1) A shape rotated about the x- - axis would be : y n (Cx)2 dx 2) A shape rotated about the y- axis wolud be V= 7 f (y) 2 dy C