MAT136H1 Lecture : 6.2 Volumes Question #1 (Easy)
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Question #1 (easy): finding the volume of a solid rotated about a horizontal line. To find the volume of a solid, first the area expression for the base needs to be established: When the solid is obtained from the area bound by two functions, he shape of the cross-sectional area is called a washer. When these information are determined, the volume can be calculated as: ( ) Find the volume of the solid that is obtained by rotating the area bound by two functions about the given line. Include the sketch of the bound area, as well as the solid and a typical sample disk or washer. Since the rotation is about the -axis, the integration is with respect to variable . This means the functions need to be written in terms of . The functions are already given in terms of , no rearrangement is necessary. Then the expression of the area of cross-section needs to be established: