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Problem 2 - Entrance Test

Find the volume of the solid generated by revolving the region bounded by y = x^3, y = 8, and x = 0 about the y-axis.

Correct: A

Using the disk method, V = π ∫[0,8] (y^(1/3))^2 dy = π ∫[0,8] y^(2/3) dy = π [ (3/5)y^(5/3) ] from 0 to 8 = π (3/5)(32) = 96π/5.