Chernobog S.
asked • 07/27/23Applications to Geometry
Consider the region bounded by y = x2, y = 1, and the y-axis for x ≥ 0. Find the volume of the solid obtained by rotating the region around the line y = -8.
V =
Hint: Find the inner radius and outer radius of the solid.
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1 Expert Answer
Yefim S. answered • 07/28/23
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Math Tutor with Experience
v = π∫01[92 - (x2 + 8)2]dx = π∫01(17 - 16x2 - x4)dx = π(17x - 16x3/3 - x5/5)01 = π(17 - 16/3 - 1/5) = 172π/15
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Doug C.
Visit this Desmos graph to see a solution based on the washer method, then achieving the same result with the shell method. desmos.com/calculator/eclaingjul Make a comment here on any steps where you need clarification.07/28/23