Math 150B 7.2 Volumes.pdf - Section 7.2 Volumes In trying...

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Page 1of 7Section 7.2: Volumes In trying to find the volume of a solid we face the same type of problem as in finding the areas. We have an intuitive idea of what volume means, but we must make this idea precise by using calculus o give an exact definition of a volume. We start with a simple solid called a cylinder (or, more precisely, a right cylinder). As illustrated in the figure above, a cylinder is bounded by a plane region 1B, called the base, and a congruent region 2Bin a parallel plane. The cylinder consists of all point on the line segments that are perpendicular to the base and join 1Band 2B. If the area of the base is A and the height of the cylinder (the distance from 1Band 2B) is h, then the volume of the cylinder is defined as VAhIn particular, if the base is a circle with radius r, then the cylinder is a circular cylinder with volume And if the base is a rectangle, then the cylinder is a rectangular box with volume
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