Mathematics

Mathematics

Problem

A solid is formed by revolving the region under a positive function y=f(x)y=f(x) on [0,2][0,2] about the xx-axis, producing volume V1V_1. A second solid is formed by revolving the region under y=12f(x)y=\tfrac12 f(x) on the same interval about the xx-axis, producing volume V2V_2. Which of the following describes the relationship between V1V_1 and V2V_2? a) V2=18V1V_2=\dfrac18 V_1 b) V2=12V1V_2=\dfrac12 V_1 c) V2=14V1V_2=\dfrac14 V_1 d) V2=V1V_2=V_1

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