MAT 266 Lecture 15: Volume by Slicing
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Mat266 lecture #15 7. 2 volume by slicing. Step 1: figure out how to slice the solid: choose a variable to indicate the position of 0ther pieces. Step 2: find out the area of the cross section at the position x. Example: volume of a cone: slice the cone horizontally, find the area of the slice at height q. Use this because the cross section is a circle. Example 2: find a formula for the volume of a pyramid whose height h and base is a square l*l. Figure: slice the solid horizontally, find the area of the cross section at height k. Example 3: find the volume of the solid whose base is the region in the xy plane bounded by y=ex , x-axis, and x=1 and the y-axis. The cross section is perpendicular to the x-axis and forms semi-circles. The area of the cross section through x is: