Find the volume of the solid obtained by rotating the region bounded by the given curves about the speciﬁed axis. y = 64x-8x^2, y = 0; about the y-axis.

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Mathematics

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8 December, 00:46

Find the volume of the solid obtained by rotating the region bounded by the given curves about the speciﬁed axis. y = 64x-8x^2, y = 0; about the y-axis.

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Keagan Brady · Answer 1

We need to get the limits first. When y = 0

0 = 64x - 8x^2

x = 0 and x = 8

The volume is

V = ∫ y dx from 0 to 8

V = ∫ (64x - 8x^2) dx from 0 to 8

V = 32x^2 - 8x^3/3 from 0 to 8

V = 682.67